Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Random-field Potts model with dipolarlike interactions: Hysteresis avalanches and microstructure

A model for the study of hysteresis and avalanches in a first-order phase transition from a single variant phase to a multivariant phase is presented. The model is based on a modification of the random-field Potts model with metastable dynamics by adding a dipolar interaction term truncated at nearest neighbors. We focus our study on hysteresis loop properties, on the three-dimensional microstructure formation, and on avalanche statistics.

Formal theory building for the avalanche game: explaining counter-intuitive behaviour of a complex system using geometrical and human behavioural/physiological effects

In 'Avalanche', an object is lowered, players staying in contact throughout. Normally the task is easily accomplished. However, with larger groups counter-intuitive behaviours appear. The paper proposes a formal theory for the underlying causal mechanisms. The aim is to not only provide an explicit, testable hypothesis for the source of the observed modes of behaviour-but also to exemplify the contribution that formal theory building can make to understanding complex social phenomena. Mapping reveals the importance of geometry to the Avalanche game; each player has a pair of balancing loops, one involved in lowering the object, the other ensuring contact. For more players, sets of balancing loops interact and these can allow dominance by reinforcing loops, causing the system to chase upwards towards an ever-increasing goal. However, a series of other effects concerning human physiology and behaviour (HPB) is posited as playing a role. The hypothesis is therefore rigorously tested using simulation. For simplicity a 'One Degree of Freedom' case is examined, allowing all of the effects to be included whilst rendering the analysis more transparent. Formulation and experimentation with the model gives insight into the behaviours. Multi-dimensional rate/level analysis indicates that there is only a narrow region in which the system is able to move downwards. Model runs reproduce the single 'desired' mode of behaviour and all three of the observed 'problematic' ones. Sensitivity analysis gives further insight into the system's modes and their causes. Behaviour is seen to arise only when the geometric effects apply (number of players greater than degrees of freedom of object) in combination with a range of HPB effects. An analogy exists between the co-operative behaviour required here and various examples: conflicting strategic objectives in organizations; Prisoners' Dilemma and integrated bargaining situations. Additionally, the game may be relatable in more direct algebraic terms to situations involving companies in which the resulting behaviours are mediated by market regulations. Finally, comment is offered on the inadequacy of some forms of theory building and the case is made for formal theory building involving the use of models, analysis and plausible explanations to create deep understanding of social phenomena.

Photoelectron multipliers based on avalanche pn - i - pn structures

We present a new physical principle to design an optoelectronic device, which consists of a multilayered semiconductor structure, where the necessary conditions for generation of photoelectrons are met, such that it will enable sequential avalanche multiplication of electrons and holes inside two depletion slabs created around the p - n junctions of a reverse biased pn - i - pn structure. The mathematical model and computer simulations of this Semiconductor Photo-electron Multiplier (SPEM) for different semiconductor materials are presented. Its performance is evaluated and compared with that of conventional devices. The Geiger operational mode is briefly discussed which may be used in Silicon Photomultiplier (SiPM) as an elementary photo detector to enhance its performance.

Temporal variability of damage potential on roads as a conceptual contribution towards a short-term avalanche risk simulation

The fatality risk caused by avalanches on road networks can be analysed using a long-term approach, resulting in a mean value of risk, and with emphasis on short-term fluctuations due to the temporal variability of both, the hazard potential and the damage potential. In this study, the approach for analysing the long-term fatality risk has been adapted by modelling the highly variable short-term risk. The emphasis was on the temporal variability of the damage potential and the related risk peaks. For defined hazard scenarios resulting from classified amounts of snow accumulation, the fatality risk was calculated by modelling the hazard potential and observing the traffic volume. The avalanche occurrence probability was calculated using a statistical relationship between new snow height and observed avalanche releases. The number of persons at risk was determined from the recorded traffic density. The method resulted in a value for the fatality risk within the observed time frame for the studied road segment. The long-term fatality risk due to snow avalanches as well as the short-term fatality risk was compared to the average fatality risk due to traffic accidents. The application of the method had shown that the long-term avalanche risk is lower than the fatality risk due to traffic accidents. The analyses of short-term avalanche-induced fatality risk provided risk peaks that were 50 times higher than the statistical accident risk. Apart from situations with high hazard level and high traffic density, risk peaks result from both, a high hazard level combined with a low traffic density and a high traffic density combined with a low hazard level. This provided evidence for the importance of the temporal variability of the damage potential for risk simulations on road networks. The assumed dependence of the risk calculation on the sum of precipitation within three days is a simplified model. Thus, further research is needed for an improved determination of the diurnal avalanche probability. Nevertheless, the presented approach may contribute as a conceptual step towards a risk-based decision-making in risk management.

Conceptual Foundations of Construction of the Models and Procedures for Prediction of the Avalanche-dangerous Situations Initiation

The conceptual foundations of the models and procedures for prediction of the avalanche-dangerous situations initiation are considered. The interpretation model for analysis of the avalanche-dangerous situations initiation based on the definition of probabilities of correspondence of studied parameters to the probabilistic distributions of avalanche-dangerous or avalanche non-dangerous situations is offered. The possibility to apply such a model to the real data is considered. The main approaches to the use of multiple representations for the avalanche dangerous situations initiation analysis are generalized.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.