arXiv subjects

Pavel Polyakov

Publications and source records attributed to Pavel Polyakov.

3 recordsLinked to original sources

arXiv2026

Identification of the length scale parameter of simplified strain gradient elasticity from standard Mode I fracture tests

Recently, it was shown that additional material constants of strain gradient elasticity (SGE) can be identified for brittle and quasi-brittle materials based on the analysis of experimental data on the crack size effect. In the present paper, we perform precise numerical simulations within SGE and derive regression relations for processing experimental data from standard fracture mechanics tests under pure Mode I loading conditions (CCT, SENT, SENB). We consider the simplified SGE, whose constitutive relations contain a single length scale parameter $\ell$ in addition to the classical elastic constants. We show that, for brittle materials, this parameter can be explicitly identified as $\ell \approx 0.362 (K_{Ic}/\sigma_{ult})^2$. This identification ensures that the fracture loads predicted by classical linear elastic fracture mechanics (LEFM) and by the simplified SGE coincide for relatively long Mode I cracks. However, within the simplified SGE, these fracture loads are evaluated from the nonsingular stress field using the maximum principal stress criterion. For quasi-brittle materials, we derive regression relations that describe the non-classical size effect on strength. This effect is usually treated within nonlinear fracture mechanics but can be naturally captured by SGE. Examples of identification of the length scale parameter $\ell$ based on the established relations and the experimental data for chopped fiber composites and for porous and dense quasi-brittle ceramics are presented.

cond-mat.mtrl-sci↗

arXiv2018

Spatial heterogeneity analyses identify limitations of epidemic alert systems: Monitoring influenza-like illness in France

Surveillance data serving for epidemic alert systems are typically fully aggregated in space. However, epidemics may be spatially heterogeneous, undergoing distinct dynamics in distinct regions of the surveillance area. We unveil this in retrospective analyses by classifying incidence time series. We use Pearson correlation to quantify the similarity between local time series and then classify them using modularity maximization. The surveillance area is thus divided into regions with different incidence patterns. We analyzed 31 years of data on influenza-like-illness from the French system Sentinelles and found spatial heterogeneity in 19/31 influenza seasons. However, distinct epidemic regions could be identified only 4-5 weeks after the nationwide alert. The impact of spatial heterogeneity on influenza epidemiology was complex. First, when the nationwide alert was triggered, 32-41% of the administrative regions were experiencing an epidemic, while the others were not. Second, the nationwide alert was timely for the whole surveillance area, but, subsequently, regions experienced distinct epidemic dynamics. Third, the epidemic dynamics were homogeneous in space. Spatial heterogeneity analyses can provide the timing of the epidemic peak and finish, in various regions, to tailor disease monitoring and control.

q-bio.PE↗

arXiv2016

Bayesian monitoring of emerging infectious diseases

We define data analyses to monitor a change in R, the average number of secondary cases caused by a typical infected individual. The input dataset consists of incident cases partitioned into outbreaks, each initiated from a single index case. We split of the input dataset into two successive subsets, to evaluate two successive R values, according to the Bayesian paradigm. We used the Bayes factor between the model with two different R values and that with a single R value to justify that the change in R is statistically significant. We validated our approach using simulated data, generated using known R. In particular, we found that claiming two distinct R values may depend significantly on the number of outbreaks. We then reanalyzed data previously studied by Jansen et al. [Jansen et al. Science 301 (5634), 804], concerning the effective reproduction number for measles in the UK, during 1995-2002. Our analyses showed that the 1995-2002 dataset should be divided into two separate subsets for the periods 1995-1998 and 1999-2002. In contrast, Jansen et al. take this splitting point as input of their analysis. Our estimated effective reproduction numbers R are in good agreement with those found by Jansen et al. In conclusion, our methodology for detecting temporal changes in R using outbreak-size data worked satisfactorily with both simulated and real-world data. The methodology may be used for updating R in real time, as surveillance outbreak data become available.

q-bio.PE↗