NG34A-01 INVITED
Role and Nature of Intermittency and Self-Organized Criticality in Solar Phenomena
In Solar Physics, last decades demonstrated a considerable progress in understanding of both macro-scale processes (e.g., magneto-hydro-dynamic modeling of the heliosphere, magnetic field modeling in coronal structures, etc.), on the one hand, and micro-scale phenomena (e.g., turbulence of the solar plasma), on the other hand. Further progress seems to be associated with our realization of how various micro-scale processes are involved and manifested in the macro-scale behavior of the entire Sun. A similar problem unavoidably arises in studies of any other non-linear dynamical dissipative system in Nature. Such systems that can be placed in between a chaos and a completely determined structure. The goal of this talk is to show how the conceptions of intermittency, multifractality, percolation, and self-organized criticality are closely intertwined, and how they are currently elaborated in Solar Physics and help in understanding of unpredictable behavior of our closest star.
NG34A-02 INVITED
Avalanche models of solar flares
Solar flares are produced when magnetic energy is released impulsively in the solar corona. In this talk I will first review the case for flares being the outward manifestation of self-organized critical state of the solar coronal magnetic field. After briefly reviewing the observational and theoretical aspects of the problem, I will present recent results of SOC modelling of solar flares, that attempt to go beyond the classical sandpile-like cellular automaton models, and closer to the physical picture of magnetic reconnection by stressed magnetic fields.
NG34A-03
Predictability of extreme events in spatially distributed driven hierarchical systems
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements --- hierarchical organization, spatial dynamics, and external driving --- are combined in a classical age- dependent multi-type branching diffusion process with immigration. A complete analytic description of the size- and space-dependent distributions of particles is derived. We then formulate an extreme event prediction problem and determine characteristic patterns of the system behavior as an extreme event approaches. In particular, our results imply specific premonitory deviations from self-similarity, which have been heuristically observed in real-world and modeled complex systems. Our results suggest a simple universal mechanism of such premonitory patterns and natural framework for their analytic study.
NG34A-04 INVITED
Scaling, universality and spatio-temporal clustering in seismicity and rock fracture phenomena
In this talk, I will discuss new methods from nonlinear sciences and complex network theory to characterize temporal and spatio-temporal clustering of point processes with a particular focus on their application to seismicity and rock fracture. Many striking features of natural processes can be portrayed as patterns or clusters of localized events. A generic attribute in all these cases is that one event can trigger or somehow induce another one to occur - or possibly numerous further events. Sometimes, an accounting of causal connections between clustered events is explicitly rationalized by the microscopic state and rules of the dynamical system. More often than not, though, the causal connections cannot be resolved from the data at hand and remain ambiguous. Thus, one is confronted with inferring a plausible causal structure from clusters of localized events without a detailed or "fundamental" knowledge of the true microscopic dynamics. I will present a method to search for such signs of causal structure in spatio-temporal data making minimal a priori assumptions about the underlying microscopic dynamics. For earthquakes, the method allows to recover the scaling of the rupture length with magnitude. Moreover, I will present a detailed statistical analysis of acoustic emission time series from a range of rock fracture experiments. In all considered cases, the waiting time distribution can be described by a unique scaling function indicating its universality. This scaling function is even indistinguishable from that for earthquakes suggesting its general validity for fracture processes independent of time, space and magnitude scales.
NG34A-05
Generalized Reynolds numbers and points of contact between intermittent turbulence and Self Organized Criticality
Self Organised Criticality (SOC) has received considerable attention in the context of bursty, intermittent plasma transport and energy release in the earth's magnetotail. This phenomenology can also be characterized in the context of intermittent turbulence. Here we elucidate a key similarity, and difference, between turbulence, and SOC. In fluid turbulence a single control parameter, the Reynolds number RE, which is a function of macroscopic system variables is sufficient to quantify the transition from ordered (laminar) to disordered (turbulent) flow. We suggest that a wider class of systems has this property including Self Organized Criticality (SOC). These systems can all be driven into a state with defining characteristics: they have many degrees of freedom (d.o.f.); are driven, dissipating and out of equilibrium; are on average in a steady state; and show scaling over a large dynamic range. The Reynolds number expresses the number of d.o.f., or energy carrying modes in the system. For avalanche models exhibiting SOC, d.o.f. refer to avalanche sizes and the Reynolds number RA that we identify is simply the well known ratio of the driving rate to system dissipation rate. The SOC slowly driven interaction dominated limit is reached by taking RA to zero; we show this maximizes the number of d.o.f. in the opposite sense to fluid turbulence. This result clarifies the much debated relationship between turbulence and SOC. A corollary is that for a sufficiently large system, SOC - like behaviour can occur at finite driving rates, important if SOC is a mechanism operating in real physical systems.
NG34A-06
Scaling Properties of Fresh Snow Roughness
The roughness characteristics of snow covered surfaces are one of the key parameters influencing surface energy and mass transfer. In particular, finding relationships between surface roughness geometry and the aerodynamic roughness length z0 is very desirable since z0 is an important parameter in any numerical model designed to simulate processes of snow-atmosphere interaction. This study focuses on fresh snow roughness for which these relationships have not been developed yet. We present results coming from a series of experiments where fresh snow roughness was measured by means of image analysis. The data were then analysed by using a statistical approach based on the pth-order structure functions (p=1 to 5). We show how this simple technique allows to estimate important roughness length scales, including the average size of the falling snow particles, which can be an important parameter for snow drift models. Overall, it was noted that very often fresh snow roughness covers length scales much larger than the size of the falling snow particles. We argue that such scales are built up during snow fall and that their scaling behaviour is captured by a well known continuum growth model, i.e. the Kardar Parisi Zhang equation. This study represents the first step towards finding key roughness parameters to be used for the modelling of z0. The use of the SLF cold wind tunnel will allow to find empirical relationships between such parameters and z0. Preliminary results confirm that z0 is mostly influenced by roughness scales larger than the falling snow particles.
NG34A-07 INVITED
Self-Organised and Critical Behaviour of the Terrestrial Magnetosphere from High- to Low- Latitudes
In a series of previous publications it has been shown that spatiotemporal activity in the high-latitude terrestrial magnetosphere exhibits signatures of self-organized criticality (SOC), a robust multiscale stochastic regime observed in driven nonlinear systems with many coupled degrees of freedom. Here, we examine signatures of avalanching and multiscale behavior in the dynamics of geomagnetic disturbances at low-latitudes. The ensemble average dynamics of activity bursts in the low-latitude fluctuations are scale-free and are characterized by consistent values of critical spreading scaling exponents. These results suggest that the inner magnetosphere operates in a nonequilibrium critical state possibly associated with SOC-like conditions in the solar wind/magnetosphere/ionosphere system. During solar maximum it appears that the scaling properties of the low-latitude magnetosphere are not purely a direct response to the scale-free properties of the solar wind but are due to inherent properties of the magnetosphere. http://faculty.erau.edu/wanlib01/writing.html
NG34A-08
An Ising Model for the Earth´s Dipole
Models for the Earth´s liquid core, and in particular, for reversals it produces, are interesting not only from the fundamental point of view but also in order to generate synthetic data (given that the set of known reversals is unique and small). We simulated the complex behavior of the Earth´s liquid core by the relatively simple Ising model (ferromagnetic). We have focused our attention on reversals and their distribution functions. Each ring current was supposed to behave as a magnetic spin while the magnetization of the model was supposed to be proportional to the Earth´s dipole. We compare our results to those by Ito and Seki, the first who used this type of simulation. With that purpose they used the Q2R updating scheme. We have reproduced those simulations and obtained similar results. We have also simulated the 2D Ising system using Metropolis algorithms. Our results seem to better reproduce actual properties of reversals (in particular, the small frequency of near zero magnetization periods). A more realistic approach to simulate eddies is an antiferromagnetic model (neighbor ring currents interact in this way both mechanically and magnetically). Unfortunately the magnetization is not a good order parameter for Ising antiferromagnetic systems and the results are meaningless. A step forward was to simulate the 2D Ising antiferrimagnetic model. Results for this case are also satisfactory when compared to actual reversal distributions. The lack of dynamical ingredients (apparent in actual reversals) is, however, a drawback for these types of models. Some possible trends for future works are advanced.