Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

Blast load variability and accuracy of blast load prediction models

A statistical analysis of explosive blast loading field (test) data has revealed a high level of variability of peak reflected pressure, impulse and time of positive phase duration for repeatable tests where variability would be expected to be a minimum. The model error (accuracy) of a widely used predictive blast load model is also assessed. A probabilistic model of blast loading is then developed that considers variability and/or uncertainty of explosive mass, net equivalent quantity of an explosive in terms of TNT mass, stand-off distance, air temperature, air pressure, inherent variability and model error. Two widely used explosives are considered: Tritonal (military) and ANFO (terrorism). This type of statistical and probabilistic analysis is essential for structural reliability analysis of structures subject to explosive blast loading where load variability is an important contributor to damage and safety risks. It was found that the TM5-1300 design values for peak reflected pressure and time of positive phase duration adequately represent median values of the probability distribution of blast loads. The TM5-1300 design values for peak reflected impulse were 40% higher than median values with probabilities of exceedance of only 4% to 23%. This over-estimation of actual blast loads on a structure may lead to conservative design outcomes