A review of power laws in real life phenomena

Power law distributions, also known as heavy tail distributions, model distinct real life phenomena in the areas of biology, demography, computer science, economics, information theory, language, and astronomy, amongst others. In this paper, it is presented a review of the literature having in mind applications and possible explanations for the use of power laws in real phenomena. We also unravel some controversies around power laws.

A straightforward method to obtain the cohesive laws of bonded joints under mode I loading

A simple procedure to measure the cohesive laws of bonded joints under mode I loading using the double cantilever beam test is proposed. The method only requires recording the applied load–displacement data and measuring the crack opening displacement at its tip in the course of the experimental test. The strain energy release rate is obtained by a procedure involving the Timoshenko beam theory, the specimen’s compliance and the crack equivalent concept. Following the proposed approach the influence of the fracture process zone is taken into account which is fundamental for an accurate estimation of the failure process details. The cohesive law is obtained by differentiation of the strain energy release rate as a function of the crack opening displacement. The model was validated numerically considering three representative cohesive laws. Numerical simulations using finite element analysis including cohesive zone modeling were performed. The good agreement between the inputted and resulting laws for all the cases considered validates the model. An experimental confirmation was also performed by comparing the numerical and experimental load–displacement curves. The numerical load–displacement curves were obtained by adjusting typical cohesive laws to the ones measured experimentally following the proposed approach and using finite element analysis including cohesive zone modeling. Once again, good agreement was obtained in the comparisons thus demonstrating the good performance of the proposed methodology.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Gender inequities in portuguese state administration: how expressive feminization and facilitating laws are not enough to guarantee effective gender equity at public work

Comunicação apresentada na 69th ASPA Anual Conference, em Dalas, Texas de 7 a 11 de março de 2008

Static laws in dynamic environments (bridging science to legislation)

Proceedings of the First International Conference on Coastal Conservation and Management in the Atlantic and Mediterranean, p. 193-200

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Multidimensional schemes for hyperbolic conservation laws on triangular meshes

Genuinely multidimensional schemes, hyperbolic systems, wave equations, Euler equations, evolution Galerkin schemes, space-time conservative methods, high order accuracy, shock solutions

Zoonomia; or, The Laws of Organic Life ... by Erasmus Darwin ...

2

Zoonomia; or, The Laws of Organic Life ... by Erasmus Darwin ...

1

Numerical methods for multiphase mixture conservation laws with phase transition

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Power laws and scaling of rain events and dry spells in the Catalonia region

We analyze the statistics of rain-event sizes, rain-event durations, and dry-spell durations in a network of 20 rain gauges scattered in an area situated close to the NW Mediterranean coast. Power-law distributions emerge clearly for the dryspell durations, with an exponent around 1.50 ± 0.05, although for event sizes and durations the power-law ranges are rather limited, in some cases. Deviations from power-law behavior are attributed to finite-size effects. A scaling analysis helps to elucidate the situation, providing support for the existence of scale invariance in these distributions. It is remarkable that rain data of not very high resolution yield findings in agreement with self-organized critical phenomena.

Pandemic influenza control in Europe and the constraints resulting from incoherent public health laws.

Background With the emergence of influenza H1N1v the world is facing its first 21st century global pandemic. Severe Acute Respiratory Syndrome (SARS) and avian influenza H5N1 prompted development of pandemic preparedness plans. National systems of public health law are essential for public health stewardship and for the implementation of public health policy[1]. International coherence will contribute to effective regional and global responses. However little research has been undertaken on how law works as a tool for disease control in Europe. With co-funding from the European Union, we investigated the extent to which laws across Europe support or constrain pandemic preparedness planning, and whether national differences are likely to constrain control efforts. Methods We undertook a survey of national public health laws across 32 European states using a questionnaire designed around a disease scenario based on pandemic influenza. Questionnaire results were reviewed in workshops, analysing how differences between national laws might support or hinder regional responses to pandemic influenza. Respondents examined the impact of national laws on the movements of information, goods, services and people across borders in a time of pandemic, the capacity for surveillance, case detection, case management and community control, the deployment of strategies of prevention, containment, mitigation and recovery and the identification of commonalities and disconnects across states. Results Results of this study show differences across Europe in the extent to which national pandemic policy and pandemic plans have been integrated with public health laws. We found significant differences in legislation and in the legitimacy of strategic plans. States differ in the range and the nature of intervention measures authorized by law, the extent to which borders could be closed to movement of persons and goods during a pandemic, and access to healthcare of non-resident persons. Some states propose use of emergency powers that might potentially override human rights protections while other states propose to limit interventions to those authorized by public health laws. Conclusion These differences could create problems for European strategies if an evolving influenza pandemic results in more serious public health challenges or, indeed, if a novel disease other than influenza emerges with pandemic potential. There is insufficient understanding across Europe of the role and importance of law in pandemic planning. States need to build capacity in public health law to support disease prevention and control policies. Our research suggests that states would welcome further guidance from the EU on management of a pandemic, and guidance to assist in greater commonality of legal approaches across states.