Grand minima and maxima of solar activity: New observational constraints

Using a reconstruction of sunspot numbers stretching over multiple millennia, we analyze the statistics of the occurrence of grand minima and maxima and set new observational constraints on long-term solar and stellar dynamo models. We present an updated reconstruction of sunspot number over multiple millennia, from $^{14}$C data by means of a physics-based model, using an updated model of the evolution of the solar open magnetic flux. A list of grand minima and maxima of solar activity is presented for the Holocene (since 9500 BC) and the statistics of both the length of individual events as well as the waiting time between them are analyzed. The occurrence of grand minima/maxima is driven not by long-term cyclic variability, but by a stochastic/chaotic process. The waiting time distribution of the occurrence of grand minima/maxima deviates from an exponential distribution, implying that these events tend to cluster together with long event-free periods between the clusters. Two different types of grand minima are observed: short (30--90 years) minima of Maunder type and long ($>$110 years) minima of Sp\"orer type, implying that a deterministic behaviour of the dynamo during a grand minimum defines its length. The duration of grand maxima follows an exponential distribution, suggesting that the duration of a grand maximum is determined by a random process. These results set new observational constraints upon the long-term behaviour of the solar dynamo.Comment: 10 Figure

Solar Grand Minima and random fluctuations in dynamo parameters

We consider to what extent the long-term dynamics of cyclic solar activity in the form of Grand Minima can be associated with random fluctuations of the parameters governing the solar dynamo. We consider fluctuations of the alpha-coefficient in the conventional Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and demonstrate that they can mimic the gross features of the phenomenon of the occurrence of Grand Minima over a suitable parameter range. The temporal distribution of these Grand Minima appears chaotic, with a more or less exponential waiting time distribution, typical of Poisson processes. In contrast however, the available reconstruction of Grand Minima statistics based on cosmogenic isotope data demonstrates substantial deviations from this exponential law. We were unable to reproduce the non-Poissonic tail of the waiting time distribution either in the framework of a simple alpha-quenched Parker model, or in its straightforward generalization, nor in simple models with feedback on the differential rotation. We suggest that the disagreement may only be apparent and is plausibly related to the limited observational data, and that the observations and results of numerical modeling can be consistent and represent physically similar dynamo regimes.Comment: Solar Physics, in prin

Achievements and Challenges in the Science of Space Weather

In June 2016 a group of 40 space weather scientists attended the workshop on Scientific Foundations of Space Weather at the International Space Science Institute in Bern. In this lead article to the volume based on the talks and discussions during the workshop we review some of main past achievements in the field and outline some of the challenges that the science of space weather is facing today and in the future.Peer reviewe

A developmental model for branching morphogenesis of lake cress compound leaf

Lake cress, Rorippa aquatica (Brassicaceae), is a semi-aquatic plant that exhibits a variety of leaf shapes, from simple leaves to highly branched compound leaves, depending on the environment. Leaf shape can vary within a single plant, suggesting that the variation can be explained by a simple model. In order to simulate the branched structure in the compound leaves of R. aquatica, we implemented reaction-diffusion (RD) patterning onto a theoretical framework that had been developed for serration distribution in the leaves of Arabidopsis thaliana, with the modification of the one-dimensional reaction-diffusion domain being deformed with the spatial periodicity of the RD pattern while expanding. This simple method using an iterative pattern could create regular and nested branching patterns. Subsequently, we verified the plausibility of our theoretical model by comparing it with the experimentally observed branching patterns. The results suggested that our model successfully predicted both the qualitative and quantitative aspects of the timing and positioning of branching in growing R. aquatica leaves

Microtubule formation on the nuclear surface during meiosis inAcetabularia acetabulum

Microtubules (MT) are a feature of all eukaryotic cells. However, they have not been observed in the cytoplasm of the vegetative phase ofAcetabularia acetabulum. Previous investigators have reported that, in the propagative phase, MTs function as anchors in the transport of secondary nuclei to the cap. They also form elaborate arrays around nuclei during cyst formation. The life history ofA. acetabulum is marked by changes in chromatin, the nucleolus, and the perinuclear cytoplasm. In this study light microscopical features of the nucleolus and changes in chromatin, labelled with anti-histon antibodies, were used to define the developmental stages. Anti-tubulin antibodies have been used to trace the origin and development of MTs, MTs are formed on the surface of the primary nucleus. They are organized first into short thick “sticks” and then later elongate into thinner strands which enclose the nucleus in a dense network. Following these events on the surface of the nucleus, the spindle develops inside the nuclear membrane which remains intact throughout the mitotic division