Discrete Fault Models

Fault surfaces are characterized by an inhomogeneous friction distribution, that can be represented with asperity models. Fault mechanics is dominated by asperities, so that a fruitful approach is to use discrete models, where asperities are the basic elements and the state of the fault is described by the average values of stress, friction and slip on each asperity. Under reasonable assumptions, the equations of motion can be solved analytically, with a deeper understanding of the behavior of the system. Fault dynamics has a sticking mode, where asperities are stationary, and a number of slipping modes, corresponding to the separate or simultaneous motion of asperities. Any seismic event is a sequence of slipping modes and a large variety of source functions is possible. Many large earthquakes are observed to be the consequence of the failure of two asperities: a discrete two-asperity model shows a rich dynamics and allows a detailed study of interaction between asperities. In this framework, fault evolution during coseismic and interseismic intervals can be calculated in terms of fault slip, stress state, energy release and seismic spectrum, including viscoelastic relaxation, fault creep and stress perturbations from other faults. Discrete models may include interaction between neighboring faults, allowing to assess conditions for the occurrence of seismic sequences in a fault system. A review of recent work on this subject is presented with applications to real earthquakes

Simulation of the long-term behaviour of a fault with two asperities

A system made of two sliding blocks coupled by a spring is employed to simulate the long-term behaviour of a fault with two asperities. An analytical solution is given for the motion of the system in the case of blocks having the same friction. An analysis of the phase space shows that orbits can reach a limit cycle only after entering a particular subset of the space. There is an infinite number of different limit cycles, characterized by the difference between the forces applied to the blocks or, as an alternative, by the recurrence pattern of block motions. These results suggest that the recurrence pattern of seismic events produced by the equivalent fault system is associated with a particular stress distribution which repeats periodically. Admissible stress distributions require a certain degree of inhomogeneity, which depends on the geometry of fault system. Aperiodicity may derive from stress transfers from neighboring faults

Conditions for large earthquakes in a two-asperity fault model

Abstract. A fault with two asperities is modelled as a system made of two blocks coupled by a spring and sliding on a plane under the same values of static and dynamic friction. An analytical solution is given for the simultaneous motion of the blocks and the corresponding orbits are plotted in the phase space. It is proven that, whichever the initial state is, the long-term behaviour of the system is one of an infinite number of limit cycles, characterized by a particular pattern of forces. The region where the system is located when the blocks are stationary can be divided into narrow stripes corresponding to different orbits of the points belonging to them. This implies that the system is sensitive to perturbations and has relevant implications for a fault, which is subject to stress transfers from earthquakes generated by neighbouring faults. In this case, the fault may experience a larger earthquake, with the simultaneous failure of the two asperities, which restores a stress distribution compatible with periodic behaviour. The seismic moment associated with simultaneous asperity failure is always greater than the maximum value that can be released in a limit cycle. For strongly coupled asperities, the moment can be several times larger

Dynamics of a seismogenic fault subject to variable strain rate

Abstract. The behaviour of seismogenic faults is generally investigated under the assumption that they are subject to a constant strain rate. We consider the effect of a slowly variable strain rate on the recurrence times of earthquakes generated by a single fault. To this aim a spring-block system is employed as a low-order analog of the fault. Two cases are considered: a sinusoidal oscillation in the driver velocity and a monotonic change from one velocity value to another. In the first case, a study of the orbit of the system in the state space suggests that the seismic activity of the equivalent fault is organized into cycles that include several earthquakes and repeat periodically. Within each cycle the recurrence times oscillate about an average value equal to the recurrence period for constant strain rate. In the second case, the recurrence time changes gradually from the value before the transition to the value following it. Asymptotic solutions are also given, approximating the case when the amplitude of the oscillation or of the monotonic change is much smaller than the average driver velocity and the period of oscillation or the duration of the transition is much longer than the recurrence times of block motions. If the system is not isolated but is subject to perturbations in stress, the perturbation anticipates or delays the subsequent earthquake. The effects of stress perturbations in the two cases of strain rate oscillations and monotonic change are considered

Dynamics of a two-fault system with viscoelastic coupling

Abstract. A fault system made of two segments or asperities subject to a constant strain rate is considered. The fault is modelled as a discrete dynamical system made of two blocks coupled by a Maxwell spring dashpot element and pulled at constant velocity on a rough plane. The long-term behaviour of the fault is studied by calculating the orbits of the system in the phase space. The model shows the role of viscoelastic relaxation in the Earth's crust in controlling the occurrence times of earthquakes. If a viscoelastic coupling is present, earthquakes are anticipated or delayed with respect to the elastic case. The limit cycles made of two alternate asperity failures, which are observed in the case of purely elastic coupling, are no longer produced. The model is applied to the 1964 Alaska earthquake, which was the effect of the failure of two asperities and for which a remarkable post-seismic relaxation has been observed in the subsequent decades. In such a fault system, viscoelastic coupling of the asperities appears to have a great influence on the occurrence times of earthquakes

Stress states and moment rates of a two-asperity fault in the presence of viscoelastic relaxation

Abstract. A fault containing two asperities with different strengths is considered. The fault is embedded in a shear zone subject to a constant strain rate by the motions of adjacent tectonic plates. The fault is modelled as a discrete dynamical system where the average values of stress, friction and slip on each asperity are considered. The state of the fault is described by three variables: the slip deficits of the asperities and the viscoelastic deformation. The system has four dynamic modes, for which analytical solutions are calculated. The relationship between the state of the fault before a seismic event and the sequence of slipping modes in the event is enlightened. Since the moment rate depends on the number and sequence of slipping modes, the knowledge of the source function of an earthquake constrains the orbit of the system in the phase space. If the source functions of a larger number of consecutive earthquakes were known, the orbit could be constrained more and more and its evolution could be predicted with a smaller uncertainty. The model is applied to the 1964 Alaska earthquake, which was the effect of the failure of two asperities and for which a remarkable post-seismic relaxation has been observed in the subsequent decades. The evolution of the system after the 1964 event depends on the state from which the event was originated, that is constrained by the observed moment rate. The possible durations of the interseismic interval and the possible moment rates of the next earthquake are calculated as functions of the initial state

Aspect-Based Sentiment Analysis Using a Two-Step Neural Network Architecture

The World Wide Web holds a wealth of information in the form of unstructured texts such as customer reviews for products, events and more. By extracting and analyzing the expressed opinions in customer reviews in a fine-grained way, valuable opportunities and insights for customers and businesses can be gained. We propose a neural network based system to address the task of Aspect-Based Sentiment Analysis to compete in Task 2 of the ESWC-2016 Challenge on Semantic Sentiment Analysis. Our proposed architecture divides the task in two subtasks: aspect term extraction and aspect-specific sentiment extraction. This approach is flexible in that it allows to address each subtask independently. As a first step, a recurrent neural network is used to extract aspects from a text by framing the problem as a sequence labeling task. In a second step, a recurrent network processes each extracted aspect with respect to its context and predicts a sentiment label. The system uses pretrained semantic word embedding features which we experimentally enhance with semantic knowledge extracted from WordNet. Further features extracted from SenticNet prove to be beneficial for the extraction of sentiment labels. As the best performing system in its category, our proposed system proves to be an effective approach for the Aspect-Based Sentiment Analysis

Biodegradable and drug-eluting inorganic composites based on mesoporous zinc oxide for urinary stent applications

Conventional technologies for ureteral stent fabrication suffer from major inconveniences such as the development of encrustations and bacteria biofilm formation. These drawbacks typically lead to the failure of the device, significant patient discomfort and an additional surgery to remove and replace the stent in the worst cases. This work focuses on the preparation of a new nanocomposite material able to show drug elution properties, biodegradation and eventually potential antibacterial activity. Poly(2-hydroxyethyl methacrylate) or the crosslinked poly(2-hydroxyethyl methacrylate)-co-poly(acrylic acid) hydrogels were prepared by the radical polymerization method and combined with a biodegradable and antibacterial filling agent, i.e., flower-like Zinc Oxide (ZnO) micropowders obtained via the hydrothermal route. The physico-chemical analyses revealed the correct incorporation of ZnO within the hydrogel matrix and its highly mesoporous structure and surface area, ideal for drug incorporation. Two different anti-inflammatory drugs (Ibuprofen and Diclofenac) were loaded within each composite and the release profile was monitored up to two weeks in artificial urine (AU) and even at different pH values in AU to simulate pathological conditions. The addition of mesoporous ZnO micropowders to the hydrogel did not negatively affect the drug loading properties of the hydrogel and it was successfully allowed to mitigate undesirable burst-release effects. Furthermore, the sustained release of the drugs over time was observed at neutral pH, with kinetic constants (k) as low as 0.05 h-1. By exploiting the pH-tunable swelling properties of the hydrogel, an even more sustained release was achieved in acidic and alkaline conditions especially at short release times, with a further reduction of burst effects (k ≈ 0.01-0.02 h-1). The nanocomposite system herein proposed represents a new material formulation for preparing innovative drug eluting stents with intrinsic antibacterial properties

An MRI volumetric study for leg muscles in congenital clubfoot

PURPOSE: To investigate both volume and length of the three muscle compartments of the normal and the affected leg in unilateral congenital clubfoot. METHODS: Volumetric magnetic resonance imaging (VMRI) of the anterior, lateral and postero-medial muscular compartments of both the normal and the clubfoot leg was obtained in three groups of seven patients each, whose mean age was, respectively, 4.8 months, 11.1 months and 4.7 years. At diagnosis, all the unilateral congenital clubfeet had a Pirani score ranging from 4.5 to 5.5 points, and all of them had been treated according to a strict Ponseti protocol. All the feet had percutaneous lengthening of the Achilles tendon. RESULTS: A mean difference in both volume and length was found between the three muscular compartments of the leg, with the muscles of the clubfoot side being thinner and shorter than those of the normal side. The distal tendon of the tibialis anterior, peroneus longus and triceps surae (Achilles tendon) were longer than normal on the clubfoot side. CONCLUSIONS: Our study shows that the three muscle compartments of the clubfoot leg are thinner and shorter than normal in the patients of the three groups. The difference in the musculature volume of the postero-medial compartment between the normal and the affected side increased nine-fold from age group 2 to 3, while the difference in length increased by 20 %, thus, showing that the muscles of the postero-medial compartment tend to grow in both thickness and length much less than the muscles of the other leg compartments