Onset of Localization in Heterogeneous Interfacial Failure

We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model without any detectable spatial correlations between the positions of the failing fibers until localization sets in. The onset of localization is an instability, not a phase transition. Depending on the elastic constant describing the elastic half space, localization sets in before or after the critical load causing the interface to fail completely, is reached. There is a crossover between failure due to localization or failure without spatial correlations when tuning the elastic constant, not a phase transition. Contrary to earlier claims based on models different from ours, we find that a finite fraction of fibers must fail before the critical load is attained, even in the extreme localization regime, i.e.\ for very small elastic constant. We furthermore find that the critical load remains finite for all values of the elastic constant in the limit of an infinitely large system.Comment: 4 pages, 5 figure

Breakdown of disordered media by surface loads

We model an interface layer connecting two parts of a solid body by N parallel elastic springs connecting two rigid blocks. We load the system by a shear force acting on the top side. The springs have equal stiffness but are ruptured randomly when the load reaches a critical value. For the considered system, we calculate the shear modulus, G, as a function of the order parameter, \phi, describing the state of damage, and also the ``spalled'' material (burst) size distribution. In particular, we evaluate the relation between the damage parameter and the applied force and explore the behaviour in the vicinity of material breakdown. Using this simple model for material breakdown, we show that damage, caused by applied shear forces, is analogous to a first-order phase transition. The scaling behaviour of G with \phi is explored analytically and numerically, close to \phi=0 and \phi=1 and in the vicinity of \phi_c, when the shear load is close but below the threshold force that causes material breakdown. Our model calculation represents a first approximation of a system subject to wear induced loads.Comment: 15 pages, 7 figure

Energy bursts in fiber bundle models of composite materials

As a model of composite materials, a bundle of many fibers with stochastically distributed breaking thresholds for the individual fibers is considered. The bundle is loaded until complete failure to capture the failure scenario of composite materials under external load. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We determine the distribution of bursts in which an amount of energy $E$ is released. The energy distribution follows asymptotically a universal power law $E^{-5/2}$, for any statistical distribution of fiber strengths. A similar power law dependence is found in some experimental acoustic emission studies of loaded composite materials.Comment: 5 pages, 4 fig

Comparison of Two Detailed Models of Aedes aegypti Population Dynamics

The success of control programs for mosquito-­borne diseases can be enhanced by crucial information provided by models of the mosquito populations. Models, however, can differ in their structure, complexity, and biological assumptions, and these differences impact their predictions. Unfortunately, it is typically difficult to determine why two complex models make different predictions because we lack structured side-­by-­side comparisons of models using comparable parameterization. Here, we present a detailed comparison of two complex, spatially explicit, stochastic models of the population dynamics of Aedes aegypti, the main vector of dengue, yellow fever, chikungunya, and Zika viruses. Both models describe the mosquito?s biological and ecological characteristics, but differ in complexity and specific assumptions. We compare the predictions of these models in two selected climatic settings: a tropical and weakly seasonal climate in Iquitos, Peru, and a temperate and strongly seasonal climate in Buenos Aires, Argentina. Both models were calibrated to operate at identical average densities in unperturbedconditions in both settings, by adjusting parameters regulating densities in each model (number of larval development sites and amount of nutritional resources). We show that the models differ in their sensitivityto environmental conditions (temperature and rainfall) and trace differences to specific model assumptions.Temporal dynamics of the Ae. aegypti populations predicted by the two models differ more markedly under strongly seasonal Buenos Aires conditions. We use both models to simulate killing of larvae and/or adults with insecticides in selected areas. We show that predictions of population recovery by the models differ substantially, an effect likely related to model assumptions regarding larval development and (director delayed) density dependence. Our methodical comparison provides important guidance for model improvement by identifying key areas of Ae. aegypti ecology that substantially affect model predictions, and revealing the impact of model assumptions on population dynamics predictions in unperturbed and perturbed conditions.Fil: Legros, Mathieu. University of North Carolina; Estados UnidosFil: Otero, Marcelo Javier. Universidad de Buenos Aires; ArgentinaFil: Romeo Aznar, Victoria Teresa. Universidad de Buenos Aires; ArgentinaFil: Solari, Hernan Gustavo. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Gould, Fred. National Institutes of Health; Estados UnidosFil: Lloyd, Alun L.. National Institutes of Health; Estados Unido

Interacting damage models mapped onto Ising and percolation models

We introduce a class of damage models on regular lattices with isotropic interactions, as e.g. quasistatic fiber bundles. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in elastic energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, we obtain the probability distribution of each damage configuration at any level of the imposed external deformation. We demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, we show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard Ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. We also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, we also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model to standard statistical mechanics.Comment: 16 pages, 3 figure

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

Risk factors for stress fracture in female endurance athletes : a cross-sectional study

Objective To identify psychological and physiological correlates of stress fracture in female endurance athletes. Design A cross-sectional design was used with a history of stress fractures and potential risk factors assessed at one visit. Methods Female-endurance athletes (58 runners and 12 triathletes) aged 26.0±7.4 years completed questionnaires on stress fracture history, menstrual history, athletic training, eating psychopathology and exercise cognitions. Bone mineral density, body fat content and lower leg lean tissue mass (LLLTM) were assessed using dual-x-ray absorptiometry. Variables were compared between athletes with a history of stress fracture (SF) and those without (controls; C) using χ², analysis of variance and Mann-Whitney U tests. Results Nineteen (27%) athletes had previously been clinically diagnosed with SFs. The prevalence of current a/oligomenorrhoea and past amenorrhoea was higher in SF than C (p=0.008 and p=0.035, respectively). SF recorded higher global scores on the eating disorder examination questionnaire (p=0.049) and compulsive exercise test (p=0.006) and had higher LLLTM (p=0.029) compared to C. These findings persisted with weight and height as covariates. In multivariate logistic regression, compulsive exercise, amenorrhoea and LLLTM were significant independent predictors of SF history (p=0.006, 0.009 and 0.035, respectively). Conclusions Eating psychopathology was associated with increased risk of SF in endurance athletes, but this may be mediated by menstrual dysfunction and compulsive exercise. Compulsive exercise, as well as amenorrhoea, is independently related to SF risk

The transformative potential of reflective diaries for elite English cricketers

The sport of cricket has a history of its players suffering from mental health issues. The psychological study of cricket and, in particular, the attendant demands of participating at an elite level has not previously received rigorous academic attention. This study explored ten elite male cricketers’ experiences of keeping a daily reflective diary for one month during the competitive season. The aim was to assess how valuable qualitative diaries are in this field. Participants were interviewed regarding their appraisal of the methodology as a self‐help tool that could assist coping with performance pressures and wider life challenges. Three outcomes were revealed: first, that diary keeping was an effective opportunity to reflect upon the past and enhance one’s self (both as an individual and a performer); second, that diary keeping acted as a form of release that allowed participants to progress; and third, that diary keeping allowed participants to discover personal patterns of success that increased the likeliness of optimum performance