Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Nonlinear fatigue damage model based on the residual strength degradation law

In this paper, a logarithmic expression to describe the residual strength degradation process is developed in order to fatigue test results for normalized carbon steel. The definition and expression of fatigue damage due to symmetrical stress with a constant amplitude are also given. The expression of fatigue damage can also explain the nonlinear properties of fatigue damage. Furthermore, the fatigue damage of structures under random stress is analyzed, and an iterative formula to describe the fatigue damage process is deduced. Finally, an approximate method for evaluating the fatigue life of structures under repeated random stress blocking is presented through various calculation examples.

Statistical description of pattern evolution in damage-fracture

A model of dynamical process and stochastic jump has been put forward to study the pattern evolution in damage-fracture. According to the final states of evolution processes, the evolution modes can be classified as globally stable modes (GS modes) and evolution induced catastrophic modes (ElC modes); the latter are responsible for fracture. A statistical description is introduced to clarify the pattern evolution in this paper. It is indicated that the appearance of fracture in disordered materials should be depicted by probability distribution function.

Moderate energy impact analysis combining phenomenological contact law with localised damage and integral equation method

A computational impact analysis methodology has been developed, based on modal analysis and a local contact force-deflection model. The contact law is based on Hertz contact theory while contact stresses are elastic, defines a modified contact theory to take account of local permanent indentation, and considers elastic recovery during unloading. The model was validated experimentally through impact testing of glass-carbon hybrid braided composite panels. Specimens were mounted in a support frame and the contact force was inferred from the deceleration of the impactor, measured by high-speed photography. A Finite Element analysis of the panel and support frame assembly was performed to compute the modal responses. The new contact model performed well in predicting the peak forces and impact durations for moderate energy impacts (15 J), where contact stresses locally exceed the linear elastic limit and damage may be deemed to have occurred. C-scan measurements revealed substantial damage for impact energies in the range of 30-50 J. For this regime the new model predictions might be improved by characterisation of the contact law hysteresis during the unloading phase, and a modification of the elastic vibration response in line with damage levels acquired during the impact. © 2011 Elsevier Ltd. All rights reserved.

Evolution of Localized Damage Zone in Heterogeneous Media

Evolution of localized damage zone is a key to catastrophic rupture in heterogeneous materials. In the present article, the evolutions of strain fields of rock specimens are investigated experimentally. The observed evolution of fluctuations and autocorrelations of strain fields under uniaxial compression demonstrates that the localization of deformation always appears ahead of catastrophic rupture. In particular, the localization evolves pronouncedly with increasing deformation in the rock experiments. By means of the definition of the zone with high strain rate and likely damage localization, it is found that the size of the localized zone decreases from the sample size at peak load to an eventual value. Actually, the deformation field beyond peak load is bound to suffer bifurcation, namely an elastic unloading part and a continuing but localized damage part will co-exist in series in a specimen. To describe this continuous bifurcation and localization process observed in experiments, a model on continuum mechanics is developed. The model can explain why the decreasing width of localized zone can lead stable deformation to unstable, but it still has not provided the complete equations governing the evolution of the localized zone.

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions

Harminics of evolution : the philosophy of individual life basedupon natural science, as taught by modern masters of the law

UANL

Evolution of radiographic joint damage in rituximab-treated versus TNF-treated rheumatoid arthritis cases with inadequate response to TNF antagonists

Observational studies have suggested that patients with rheumatoid arthritis (RA) who experience inadequate response to anti-tumour necrosis factor (anti-TNF) agents respond more favourably to rituximab (RTX) than to an alternative anti-TNF agent. However, the relative effectiveness of these agents on long-term outcomes, particularly in radiographic damage, remains unclear.

Cultural Diversity as a Concept of Global Law : Origins, Evolution and Prospects

“Cultural diversity” has become one of the latest buzzwords on the international policymaking scene. It is employed in various contexts – sometimes as a term close to “biological diversity”, at other times as correlated to the “exception culturelle” and most often, as a generic concept that is mobilised to counter the perceived negative effects of economic globalisation. While no one has yet provided a precise definition of what cultural diversity is, what we can observe is the emergence of the notion of cultural diversity as incorporating a distinct set of policy objectives and choices at the global level. These decisions are not confined, as one might have expected, to cultural policymaking, but rather spill over to multiple governance domains because of the complex linkages inherent to the simultaneous pursuit of economic and other societal goals that cultural diversity encompasses and has effects on. Accounting for these intricate interdependencies, the present article clarifies the origins of the concept of cultural diversity as understood in global law and traces its evolution over time. Observing the dynamics of the concept and the surrounding political and legal developments, the article explores its justification and overall impact on the global legal regime, as well as its discrete effects on different domains of policymaking, such as media, intellectual property and culture. While the analysis is legal in essence, the article is meant to speak also to a broader transdisciplinary public. The article is part of the speacial issue on ethnic diversity and cultural pluralism, which is available under the creative commons licence: http://www.mdpi.com/journal/diversity/special_issues/ethnic-diversity/.

The Trade Versus Culture Discourse: Tracing its Evolution in Global Law

The intensified flows of goods, services, peoples and ideas across borders intrinsic to globalization have had numerous and multi-faceted effects. Those affecting culture have been perhaps the most controversial, as it is more often than not difficult to identify the spill-overs across economic and non-economic areas and across borders, as it is equally hard to qualify the effects of these spill-overs as positive or negative. The debate also tends to be politically and even emotionally charged, which has so far not proven advantageous to establishing a genuine dialogue, nor to finding solutions. This contention and the divergent interests of major players in the international community have been reflected in the institutions and rules of global law. It is the objective of this chapter to explore this institutional architecture, in particular its main (and opposing) constituent fora of the World Trade Organization (WTO) and the United Nations Educational Social and Cultural Organization (UNESCO). The chapter traces the evolution of these institutions and their interaction over time, as well as the underlying objectives, demands and strategies of the key proponents in the trade versus culture discourse, which ultimately shaped the existent law and policy. The chapter concludes with an appraisal of the present state of affairs situating the discussion into the contemporary global governance landscape.