This paper deals with the elastic energy induced by systems of straight edge dislocations in the framework of linearized plane elasticity. The dislocations are introduced as point topological defects of the displacement-gradient fields. Following the core radius approach, we introduce a parameter ? > 0 representing the lattice spacing of the crystal, we remove a disc of radius ? around each dislocation and compute the elastic energy stored outside the union of such discs, namely outside the core region. Then, we analyze the asymptotic behaviour of the elastic energy as ?

We consider a simple discrete model for screw dislocations in crystals. Using a variational discrete scheme we study the motion of a configuration of dislocations toward low energy configurations. We deduce an effective fully overdamped dynamics that follows the maximal dissipation criterion introduced in Cermelli and Gurtin (1999) and predicts motion along the glide directions of the crystal. (C) 2016 Elsevier Inc. All rights reserved.

We consider a simple discrete model for screw dislocations in crystals. Using a variational discrete scheme we study the motion of a configuration of dislocations toward low energy configurations. We deduce an effective fully overdamped dynamics that follows the maximal dissipation criterion introduced in Cermelli and Gurtin (1999) and predicts motion along the glide directions of the crystal. (C) 2016 Elsevier Ltd. All rights reserved.

The aim of this paper is to deepen the application of value at risk in the cyber domain, with particular attention to its potential role in security investment valuation. Cyber risk is a fundamental component of the overall risk faced by any organization. In order to plan the size of security investments and to estimate the consequent risk reduction, managers strongly need to quantify it. Accordingly, they can decide about the possibility of sharing residual risk with a third party, such as an insurance company.

We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (Heitmann and Radin in J Stat Phys 22(3):281-287, 1980), which concerns a system of N identical atoms in two dimensions interacting via the idealized pair potential if , if , 0 if .

A novel model is here introduced for theSOC change indexdefinedas the normalized difference between the actual Soil Organic Carbon and thevalue assumed at an initial reference year. It is tailored on the RothC carbonmodel dynamics and assumes as baseline the value of the SOC equilibriumunder constant environmental conditions. A sensitivity analysis is performedto evaluate the response of the model to changes of temperature, Net PrimaryProduction (NPP), and land use soil class (forest, grassland, arable).

The Internet evolution is one of the greatest innovations of the twentieth century and has changed lives of individuals and business organizations. On the other hand, potential attacks on the information systems and eventual crash may cause heavy losses on data, services and business operation. Executives and security professionals are accepting that it is not a matter of if but a matter of when their organization will be hit by a cyber-attack. As a consequence, cyber risk is a fast-growing area of concern.

Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous (both in space and time) right-hand side. The model is specifically designed to reproduce self-organized spontaneous sudden changes of direction, not caused by external stimuli like predator's attacks. The main novelty of the model is that every bird is a potential turn initiator, thus leadership is formed in a group of indistinguishable agents.

We apply the Z-control approach to a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend awareness must display over time in order to eradicate the disease.

In this work, we study the impact of high-energy radiation induced by solar X-ray flares on the determination of the temporal change in precipitable water vapor (?PWV) as estimated using the synthetic aperture radar (SAR) meteorology technique. As recent research shows, this radiation can significantly affect the ionospheric D-region and induces errors in the estimation of the total electron content (TEC) by the applied models.