Thermodynamically consistent continuum dislocation dynamics

Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i) to represent dislocation kinematics in terms of a reasonable number of variables and (ii) to derive averaged descriptions of the dislocation dynamics (i.e. material laws) in terms of these variables. The kinematic problem (i) was recently solved through the introduction of continuum dislocation dynamics (CDD), which provides kinematically consistent evolution equations of dislocation alignment tensors, presuming a given average dislocation velocity (Hochrainer (2015), Philos. Mag. 95 (12), 1321--1367). In the current paper we demonstrate how a free energy formulation may be used to solve the dynamic closure problem (ii) in CDD. We do so exemplarily for the lowest order CDD variant for curved dislocations in a single slip situation. In this case, a thermodynamically consistent average dislocation velocity is found to comprise five mesoscopic shear stress contributions. For a postulated free energy expression we identify among these stress contributions a back-stress term and a line-tension term, both of which have already been postulated for CDD. A new stress contribution occurs which is missing in earlier CDD models including the statistical continuum theory of straight parallel edge dislocations (Groma et al. (2015), Acta Mater. 51, 1271-1281). Furthermore, two entirely new stress contributions arise from the curvature of dislocations

Systemic and Extreme Risks:Ways Forward for a Joint Framework

Systemic risk is getting increasing attention in the science as well as popular press not to the least due to the growing complexity of the world as well as increasing data availability. The aim of this paper is to discuss selected topics in extreme and systemic risk modelling, measuring and management approaches.We find that from a purely quantitative modelling perspective, single and systemic risk assessment can be jointly performed via the concept of copulas and therefore can be embedded within an integrated framework without major difficulties. Consequently, we see single and systemic risks as not independent but indivisible which have to be assessed jointly. However, from a risk measure perspective we see some important differences as single risk measures focus on probability distributions while systemic risk measures focus on dependency measures. Hence, we call for ensembles of risk measures which should be a superior approach for studying single and systemic risks in complex networks as different events can cause systemic risk to realize (e.g. too big to fail, too interconnected to fail, keystone species etc.). From a risk management perspective, we conclude that the inclusion of human agents causes a fundamental difference in the management of systemic risks compared to other systems as their decisions are contingent and may cause unpredictable shifts due to mutual uncertainties that can evolve. Consequently, we argue for an iterative risk management approach similar to the call from climate change and adaptation science, for example discussed in the various IPCC reports. Last but not least, the idea of collective responsibility echoes the need to target risks that threaten whole societies. That such risks are reduced is foremost in the public interest and we therefore call for an institutional change that enables the effective handling of it in the future

Nonclassicality of induced coherence without induced emission

Interference of two beams produced at separate biphoton sources was first observed more than two decades ago. The phenomenon, often called "induced coherence without induced emission", has recently gained attention after its applications to imaging, spectroscopy, and measuring biphoton correlations have been discovered. The sources used in the corresponding experiments are nonlinear crystals pumped by laser light. The use of a laser pump makes the occurrence of induced (stimulated) emission unavoidable and the effect of stimulated emission can be observed in the joint detection rate of the two beams. This fact raises the question whether the stimulated emission also lays a role in inducing the coherence. Here we investigate a case in which the crystals are pumped with a single-photon Fock state. We find that coherence is induced even though the possibility of stimulated emission is now fully ruled out. Furthermore, the joint detection rate of the two beams becomes ideally zero and does no longer change with the pump power. We illustrate our results by numerical simulations and by comparisons with experimental findings. Our results rule out any classical or semi-classical explanation of the phenomenon and also imply that similar experiments can be performed with fermions, for which stimulated emission is strictly forbidden.Comment: 8 pages, 3 figure

Assessing the financial vulnerability to climate-related natural hazards

National governments are key actors in managing the impacts of extreme weather events, yet many highly exposed developing countries -- faced with exhausted tax bases, high levels of indebtedness, and limited donor assistance -- have been unable to raise sufficient and timely capital to replace or repair damaged infrastructure and restore livelihoods after major disasters. Such financial vulnerability hampers development and exacerbates poverty. Based on the record of the past 30 years, this paper finds many developing countries, in particular small island states, to be highly financially vulnerable, and experiencing a resource gap (net disaster losses exceed all available financing sources) for events that occur with a probability of 2 percent or higher. This has three main implications. First, efforts to reduce risk need to be ramped-up to lessen the serious human and financial burdens. Second, contrary to the well-known Arrow-Lind theorem, there is a case for country risk aversion implying that disaster risks faced by some governments cannot be absorbed without major difficulty. Risk aversion entails the ex ante financing of losses and relief expenditure through calamity funds, regional insurance pools, or contingent credit arrangements. Third, financially vulnerable (and generally poor) countries are unlikely to be able to implement pre-disaster risk financing instruments themselves, and thus require technical and financial assistance from the donor community. The cost estimates of financial vulnerability -- based on today's climate -- inform the design of"climate insurance funds"to absorb high levels of sovereign risk and are found to be in the lower billions of dollars annually, which represents a baseline for the incremental costs arising from future climate change.Hazard Risk Management,Debt Markets,Insurance&Risk Mitigation,Banks&Banking Reform,Climate Change Economics

Modelling Dependent Risk With Copulas: An Application On Flooding Using Agent-Based Modelling

In the present work we introduce a copula approach to model dependencies between risks in large scale networks and show how this could be used to avoid underestimation of extreme events. Furthermore, we apply the approach within an agent based model to determine the macroeconomic consequences due to flood events. We show that without a copula approach only average annual losses on the country level would be available. However, with the copula approach, which includes the estimation of basin scale loss distribution through catastrophe modelling, exposure estimation through Corine land cover mapping, assessment of appropriate copulas and parameter estimation, including a algorithm to couple coupled basins as well as an upscaling procedure to the country level, the whole risk spectrum can be, for the first time on this scale, estimated. The direct loss estimates from the copula approach, separated into different risk bearers, are used to build a damage scenario generator which gives the input for the agent based model. The agent based model in turn assesses the additional indirect losses due to the event which can be much larger than the direct losses alone

Modelling Macroeconomic Effects of Natural Disaster Risk: A Large Scale Agent Based Modelling Approach Using Copulas

We introduce a copula approach to model dependencies between risks and show how this could be used to avoid underestimation of extreme events in large-scale risk assessments. We apply the approach within an extensive agent based model to determine the macroeconomic consequences due to catastrophic events. The agent based approach is capable of modelling an entire national economy with all sectors, including households, firms and banks. It is based on an input-output model with 64 industries where all goods and services are produced endogenously. We show that without a copula approach only average annual losses on the country level would be available which limits analysis on long term effects. However, with the copula approach, which includes the estimation of basin scale loss distribution through catastrophe modelling, exposure estimation through Corine land cover mapping, assessment of appropriate copulas and parameter estimation, including an algorithm to couple coupled basins as well as an upscaling procedure to the country level, the whole risk spectrum can be estimated. The direct loss estimates from the copula approach, separated into different risk bearers, are used to build a damage scenario generator which gives the input for the agent based model. The agent based model in turn assesses the additional indirect losses due to the event which can be much larger than the direct losses alone. The agent based model is calibrated to the case of Austria at a scale 1: 10, e.g. with hundreds of thousands of agents and the agents are calibrated according to micro data, including business information, balance-sheets, and income statements. We show that there can be severe effects due to large scale natural disaster events through different transmission channels, even leading to systemic risks. This detailed information should be useful for determining risk management options on various scales

Evaluating Partnerships to Enhance Disaster Risk Management using Multi-Criteria Analysis: An Application at the Pan-European Level

Disaster risk is increasingly recognized as a major development challenge. Recent calls emphasize the need to proactively engage in disaster risk reduction, as well as to establish new partnerships between private and public sector entities in order to decrease current and future risks. Very often such potential partnerships have to meet different objectives reflecting on the priorities of stakeholders involved. Consequently, potential partnerships need to be assessed on multiple criteria to determine weakest links and greatest threats in collaboration. This paper takes a supranational multi-sector partnership perspective, and considers possible ways to enhance disaster risk management in the European Union by better coordination between the European Union Solidarity Fund, risk reduction efforts, and insurance mechanisms. Based on flood risk estimates we employ a risk-layer approach to determine set of options for new partnerships and test them in a high-level workshop via a novel cardinal ranking based multi-criteria approach. Whilst transformative changes receive good overall scores, we also find that the incorporation of risk into budget planning is an essential condition for successful partnerships