Characterizing and predicting the relationship between translaminar fracture toughness and pull-out length distributions under distinct temperatures.

The translaminar fracture toughness reflects the damage tolerance of a fibre-reinforced composite under longitudinal tension, which often governs the final failure of structures. One of the main energy-dissipation mechanisms that contributes to the translaminar toughness of composites is the fibre pull-out process. The present study aims to quantify and model the statistical distribution of fibre pull-out lengths formed on the translaminar fracture surface of composites, for the first time in the literature; this is done under different temperatures, so that the relationship between pull-out length distributions, micromechanical properties and the translaminar fracture toughness can be established. The fracture surfaces of cross-ply compact tension specimens tested under three different temperatures have been scanned through X-ray computed tomography to quantify the extent of fibre pull-out on the fracture surfaces; the distribution of pull-out lengths showed alarger average and larger variability with an increase in temperature, which also lead to an increase in translaminar fracture toughness. A similar trend has been captured by the proposed analytical model, which predicts the pull-out length distribution based on the analysis of quasi-fractal idealizations of the fracture surface, yielding an overall accuracy of more than 85%. This article is part of the theme issue 'Ageing and durability of composite materials'.

Impact of tuberculosis treatment length and adherence under different transmission intensities.

Tuberculosis (TB) is a leading cause of human mortality due to infectious disease. Treatment default is a relevant factor which reduces therapeutic success and increases the risk of resistant TB. In this work we analyze the relation between treatment default and treatment length along with its consequence on the disease spreading. We use a stylized model structure to explore, systematically, the effects of varying treatment duration and compliance. We find that shortening treatment alone may not reduce TB prevalence, especially in regions where transmission intensity is high, indicating the necessity of complementing this action with increased compliance. A family of default functions relating the proportion of defaulters to the treatment length is considered and adjusted to a particular dataset. We find that the epidemiological benefits of shorter treatment regimens are tightly associated with increases in treatment compliance and depend on the epidemiological background.

Estimating the effective reproduction number for heterogeneous models using incidence data.

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Periodic forcing in a three-level cellular automata model for a vector-transmitted disease.

A periodically forced two-dimensional cellular automata model is used to reproduce and analyze the complex spatiotemporal patterns observed in the transmission of vector infectious diseases. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector-transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult, and immature vector populations. The dynamics includes external seasonality forcing, human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well-defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of the absence of external periodic drive, the model predicts a completely distinct long-time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided that the forcing term takes into account the local rainfall modulation. Finally, an analysis is provided of the effect of the dependence between epidemics threshold and vector control actions, both in the presence and absence of human mobility factor.

Tsallis scaling and the long-range Ising chain: A transfer matrix approach.

A numerically efficient transfer matrix (TM) approach is introduced to investigate the long-range Ising spin chain. Results obtained within this procedure are primarily used to verify the Tsallis scaling hypothesis for long-range systems with an alpha power-law decay of the interaction constants, both in the extensive (alpha>1) and nonextensive (alpha<1) regimes. Results for finite-size systems, taking into account all interactions between spins up to 24 sites apart, show that the conjecture is satisfied with a very good precision (less than 0.004%) for all temperature intervals. This TM procedure is further used to investigate several other thermodynamic and critical properties of this system, and it may also be extended to similar one-dimensional long-range systems.

On longitudinal compressive failure of carbon-fibre-reinforced polymer: from unidirectional to woven, and from virgin to recycled.

Modelling the longitudinal compressive failure of carbon-fibre-reinforced composites has been attempted for decades. Despite many developments, no single model has surfaced to provide simultaneously a definitive explanation for the micromechanics of failure as well as validated predictions for a generic stress state. This paper explores the reasons for this, by presenting experimental data (including scanning electron microscopic observations of loaded kink bands during propagation, and brittle shear fracture at 45° to the fibres) and reviewing previously proposed micromechanical analytical and numerical models. The paper focuses mainly on virgin unidirectional (UD) composites, but studies for woven and recycled composites are also presented, highlighting similarities and differences between these cases. It is found that, while kink-band formation (also referred to in the literature as microbuckling) is predominant in UD composites under longitudinal compression, another failure mode related to the failure of the fibres can be observed experimentally. It is also shown that the micromechanics of the failure process observed in UD composites is similar to that in other fibre architectures, hence encouraging the adaptation and application of models developed for the former to the latter.

Modelling the dynamics of dengue real epidemics.

In this work, we use a mathematical model for dengue transmission with the aim of analysing and comparing two dengue epidemics that occurred in Salvador, Brazil, in 1995-1996 and 2002. Using real data, we obtain the force of infection, Λ, and the basic reproductive number, R(0), for both epidemics. We also obtain the time evolution of the effective reproduction number, R(t), which results in a very suitable measure to compare the patterns of both epidemics. Based on the analysis of the behaviour of R(0) and R(t) in relation to the adult mosquito control parameter of the model, we show that the control applied only to the adult stage of the mosquito population is not sufficient to stop dengue transmission, emphasizing the importance of applying the control to the aquatic phase of the mosquito.