NG41B-0428 0800h
Toward a Synthesis of Auroral Index Scaling Measurements
One route for study of magnetospheric energy release has been provided by scaling analysis of the Auroral Electrojet indices ($AE, AU, AL$). The scale invariance of aspects of the $AE$ index family was one-but not the sole-motivation to suggest self-organised critical ``avalanche'' scenarios of the magnetosphere. In that of Chapman $et al.$ [1998] the appearance of a characteristic scale in otherwise scale-free magnetospheric signals was identified with the properties of ``systemwide'' avalanches. It has long been recognised that the indices show a two-component nature, originally hypothesised to reflect solar wind-driven (DP2) and intrinsic (DP1) components in the ionospheric convection currents. Following the first avalanche scenarios, debate was sparked by one of the alternative possibilities, that the scale-invariant nature of the indices was due to Kolmogorov or Kraichnan scaling in solar wind MHD turbulence. We will present an up-to date review of subsequent work on scaling by the Warwick and BAS groups. We will also discuss the inter-relationships of our results with those of other workers.
NG41B-0429 0800h
Multifractal Modelling of SYM-H via Recurrent Iterated Function Systems
This paper analyzes the large-scale fluctuations of the H-component magnetic field at Earth's equator during the period from 1981-2002. A multifractal characterization is applied to the SYM-H index data and it is found that previous suggestions that SYM-H is monofractal are accurate. It is demonstrated empirically that the underlying mechanism of SYM-H, presumably ring current energization and relaxation, can be captured by recurrent iterated function systems (RIFS). The RIFS model is used to simulate the measure representation of SYM-H.
NG41B-0430 0800h
Nonlinear interaction and interactive states in a simple weak turbulence model by multiply-coupled triplets
Behavior of a nonlinear system (such as space plasma) is often discussed via evolution of eigenmodes of associated linearized system and nonlinear interactions among them. A minimum unit for representing such a nonlinear interaction is a triplet of eigenmodes, which satisfies the resonance condition. We construct a simple model of weak turbulence by multiply couple such triplets. Interestingly, this simple model has a hierarchy structure that is universal to the complex systems. Numerical study shows that the system exhibits intermittency, and long time evolution is controlled by self-organized criticality (SOC). We discuss statistics of this system by invoking the concept of the "interaction (e.g. flux between the sites)" and the "interactive state (e.g. phase difference among the sites)", and attempt to elucidate the origin of phase coherence, which appears among the eigenmodes sporadically. We also discuss properties of the intermittency observed in the time series data of the system evolution.
NG41B-0431 0800h
Thermal evolution of the Mantle: Attractor and/or repeller?
The earth has had a very complex thermal history. The mantle is now vigorously convecting but will eventually cool as heat dissipates in space.The final state can be described as an attractor because it is the fate of a dissipative systems to become uniforme or increase its entropy. The opposite is true over shorter time scales (billion years).This chaotic, non-linear system will act as a repeller. Slight changes inthe initial thermal distribution will greatly alter the final thermal distribution. This same phenomena is seen in other strongly non-linear turbulent systems such as the weather. Specifically, we test the existence of two initial conditions of mantle thermal history from a beginning of a billion years ago to present. Will it be possible for two different thermal distributions to lead to similar present conditions? Conversely, the sensitivity to initial conditions is also tested. To do this we are using a simplified but realistic model of the mantle with 2-d vertical compressibility, constant three layer rheology (400km, 650km)infinite Prandtl, constant but realistic Rayleigh Ra=10^6 to 10^7, time-dependent heating with a constant rate of radiogenic decay,constant temperature bottom boundary conditions because the exact nature of chemical-thermal core-mantle boundary is still unknown.
NG41B-0432 0800h
3D Modeling of fracture of brittle rock using Lattice Solid Model with rotational mechanism
The Lattice Solid Model (LSMearth) is a particle based model similar to the Discrete Element Model (DEM). The current LSMerath includes only radial interaction between two linked particles, involving only translational motions of particles. In this study, we extend the LSM by introducing full rigidity interactions between particles and full degrees of freedom for a single particle. In the new model, for each particle we introduce six degrees of freedom: 3 for translational motion, and 3 for orientation. Six kinds of relative motions are permitted, and six interactions are transferred, i.e., radial, two shearing forces, twisting and two bending torques. Particle motion is decomposed into translational motion of the center of mass and rotation about the center. The former is solved using conventional Molecular Dynamics algorithms. The latter is integrated using Fincham's leap-frog algorithm using quaternion representation of orientations. The relative rotation between two particles is decomposed into two sequence-independent rotations. Using such decomposition, all interactions due to the relative translational and rotational motions between interactive rigid bodies can be uniquely determined. We carried out several tests on 3-D rock failure under uni-axial compression and frictional instability between two blocks. Compared with the simulations without the single particle rotational mechanism, the new simulation results match more closely with experimental results
NG41B-0433 0800h
Stress Reorientation and LURR: Implication for Earthquake Prediction using LURR
After reviewing the problems associated with the current implementation of LURR theory, we suggest that taking account of stress field complexity and stress reorientation may resolve these problems. By introducing the concept of Maximum Faulting Orientation (MFO), we propose a new approach for calculating LURR. If the plane on which we choose to define LURR happens to be the MFO, we will obtain an LURR curve with a high peak. Otherwise, if that plane is not the MFO, the LURR anomaly may not appear, even if the plane is the main shock fault plane. Since tectonic stress may change from time to time both regionally and locally, LURR values calculated on a fixed plane will inevitably undulate. Results presented for the cases of California earthquakes provide encouragement for the stress-reorientation explanation and new approach.
NG41B-0434 0800h
Period 7.8 Years Oscillatory Modes in the Monthly NAO Index and Temperature Records and Their Possible Phase Synchronization
Recently, Gamiz-Fortis et al. (J. Geophys. Res. 107(D23) 4685, 2002) have detected, using the Monte Carlo Singular System Analysis (MCSSA), an oscillatory mode with the period around 7.7 years in the winter North Atlantic Oscillation (NAO) index. Palus and Novotna (Phys. Lett. A 248 191-202, 1998) proposed an enhancement of MCSSA in which, in addition to the signal covariance structure, a complexity measure of the SSA modes is tested against surrogate data; and were able to detect a period 7.8 years oscillatory mode in long-term monthly near-surface air temperature records from several European locations. We show that using the enhanced MCSSA the period 7.8 yr oscillatory mode can be detected in the monthly NAO index, too. These modes are extracted from the raw data (expressed in the SSA/EOF basis), their instantaneous phases are computed and their relations are studied. In particular, a possibility of phase synchronization between the NAO and the temperature oscillatory modes is tested for.