Phenomenological Growth Model Research Articles

SpatialWavePredict: a tutorial-based primer and toolbox for forecasting growth trajectories using the ensemble spatial wave sub-epidemic modeling framework

BackgroundDynamical mathematical models defined by a system of differential equations are typically not easily accessible to non-experts. However, forecasts based on these types of models can help gain insights into the mechanisms driving the process and may outcompete simpler phenomenological growth models. Here we introduce a friendly toolbox, SpatialWavePredict, to characterize and forecast the spatial wave sub-epidemic model, which captures diverse wave dynamics by aggregating multiple asynchronous growth processes and has outperformed simpler phenomenological growth models in short-term forecasts of various infectious diseases outbreaks including SARS, Ebola, and the early waves of the COVID-19 pandemic in the US.ResultsThis tutorial-based primer introduces and illustrates a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using an ensemble spatial wave sub-epidemic model based on ordinary differential equations. Scientists, policymakers, and students can use the toolbox to conduct real-time short-term forecasts. The five-parameter epidemic wave model in the toolbox aggregates linked overlapping sub-epidemics and captures a rich spectrum of epidemic wave dynamics, including oscillatory wave behavior and plateaus. An ensemble strategy aims to improve forecasting performance by combining the resulting top-ranked models. The toolbox provides a tutorial for forecasting time-series trajectories, including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score.ConclusionsWe have developed the first comprehensive toolbox to characterize and forecast time-series data using an ensemble spatial wave sub-epidemic wave model. As an epidemic situation or contagion occurs, the tools presented in this tutorial can facilitate policymakers to guide the implementation of containment strategies and assess the impact of control interventions. We demonstrate the functionality of the toolbox with examples, including a tutorial video, and is illustrated using daily data on the COVID-19 pandemic in the USA.

GrowthPredict: A toolbox and tutorial-based primer for fitting and forecasting growth trajectories using phenomenological growth models

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict, a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software (https://github.com/gchowell/forecasting_growthmodels), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

Assessing the transmission potential of mpox in East Asia during 2022-2023: A focus on Taiwan, China, Japan, and South Korea

ObjectivesThis study aims to estimate the transmission potential of mpox in East Asia, focusing on the hardest hit nations: Taiwan, China, Japan, and South Korea. MethodsWe utilized six phenomenological dynamic growth models to fit the case incidence during the initial 30 epidemic days. The best-fit model was selected to calculate the reproduction number (Rt). Additionally, we used the latest case data and a Bayesian framework to compute the instantaneous effective Rt by applying the Cori et al. method. ResultsDuring the early phase, China demonstrated the highest estimated Rt of 2.89 (95% CI: 1.44-3.33); followed by South Korea, 2.18 (95% CI: 0.96-3.57); Japan, 1.73 (95% CI: 0.66-3.94); and Taiwan, 1.36 (95% CI: 0.71-3.30). However, by June 30, 2023, estimated Rt dropped below 1.00 in all countries: China at 0.05 (95% credible interval [CrI]: 0.02-0.10), Japan at 0.32 (95% CrI: 0.15-0.59), South Korea at 0.23 (95% CrI: 0.11-0.42), and Taiwan at 0.41 (95% CrI: 0.31-0.53), indicating the potential decline of the outbreak. ConclusionsOur analysis shows effective containment by each country. It is crucial to sustain effective management to ensure the ultimate eradication of the outbreak.

Data-driven estimation of the instantaneous reproduction number and growth rates for the 2022 monkeypox outbreak in Europe.

To estimate the instantaneous reproduction number Rt and the epidemic growth rates for the 2022 monkeypox outbreaks in the European region. We gathered daily laboratory-confirmed monkeypox cases in the most affected European countries from the beginning of the outbreak to September 23, 2022. A data-driven estimation of the instantaneous reproduction number is obtained using a novel filtering type Bayesian inference. A phenomenological growth model coupled with a Bayesian sequential approach to update forecasts over time is used to obtain time-dependent growth rates in several countries. The instantaneous reproduction number Rt for the laboratory-confirmed monkeypox cases in Spain, France, Germany, the UK, the Netherlands, Portugal, and Italy. At the early phase of the outbreak, our estimation for Rt, which can be used as a proxy for the basic reproduction number R0, was 2.06 (95% CI 1.63 - 2.54) for Spain, 2.62 (95% CI 2.23 - 3.17) for France, 2.81 (95% CI 2.51 - 3.09) for Germany, 1.82 (95% CI 1.52 - 2.18) for the UK, 2.84 (95% CI 2.07 - 3.91) for the Netherlands, 1.13 (95% CI 0.99 - 1.32) for Portugal, 3.06 (95% CI 2.48 - 3.62) for Italy. Cumulative cases for these countries present subexponential rather than exponential growth dynamics. Our findings suggest that the current monkeypox outbreaks present limited transmission chains of human-to-human secondary infection so the possibility of a huge pandemic is very low. Confirmed monkeypox cases are decreasing significantly in the European region, the decline might be attributed to public health interventions and behavioral changes in the population due to increased risk perception. Nevertheless, further strategies toward elimination are essential to avoid the subsequent evolution of the monkeypox virus that can result in new outbreaks.

Phenomenological Model of SEI Formation and Growth Leveraging Real-Time Expansion Measurements

Every commercial lithium-ion battery undergoes formation at the end of the manufacturing process [1]. The formation process is time and capital-intensive, motivating battery manufacturers to develop new formation recipes to decrease formation time while preserving battery lifetime and safety [2]. Yet, despite its importance, a general framework for modeling formation of commercial lithium-ion battery systems is lacking, hindering the innovation cycle. While first-principles solid electrolyte interphase (SEI) formation modeling approaches exist [3], such models are often computationally expensive and challenging to validate, limiting their application towards predicting macroscopic variables relevant to commercial lithium-ion batteries such as capacity loss and resistance growth over life. Semi-physics based (i.e. semi-empirical, or phenomenological) approaches are popular [4], but such models are often parameterized using cell data collected after formation has already completed, making them unsuitable for capturing the initial stages of the SEI formation process.This work presents a framework for developing semi-physics based models of SEI formation and growth dynamics for use in commercial lithium-ion battery systems. The model enables real-time prediction of lithium consumption during the formation (i.e. first charge) process, which can be extended to track the lithium consumption over the entire lifespan of the cell. By explicitly considering the electrolyte reduction reaction dynamics during the first cycle, the model enables the study of how different formation protocols influence SEI passivation properties [5] and hence battery lifetime. The model leverages half-cell near-equilibrium potential curves to track the evolution of lithium stoichiometries and electrode potentials at each electrode, during and after the formation process. The model thus enables real-time tracking of the SEI-forming electrolyte reduction rates which can be used to estimate the quantity of lithium consumed to create the SEI. Model parameters are tuned against experimental electrode expansion measurements collected on NMC622|graphite pouch cells (Figure 1), which resolves both the reversible (i.e. lithiation-induced) and irreversible sources of electrode expansion [6],[7]. Model-predicted lithium consumption rates and electrode expansions are validated against an experimental dataset consisting of three different formation protocols which includes cycle life testing until the end of life.The modeling framework we propose enables practical pathways for bridging the electrochemistry of battery formation to macroscopic variables related to battery safety and lifetime, including total capacity loss, resistance growth, gas generation (during SEI and due to electrolyte oxidation at the positive electrode), and copper dissolution rates.[1] S. J. An, J. Li, C. Daniel, D. Mohanty, S. Nagpure, and D. L. Wood, “The state of understanding of the lithium-ion-battery graphite solid electrolyte interphase (SEI) and its relationship to formation cycling,” Carbon N. Y., vol. 105, pp. 52–76, 2016.[2] Y. Liu, R. Zhang, J. Wang, and Y. Wang, “Current and future lithium-ion battery manufacturing,” iScience, vol. 24, p. 102332, Apr. 2021.[3] A. Wang, S. Kadam, H. Li, S. Shi, and Y. Qi, “Review on modeling of the anode solid electrolyte interphase (SEI) for lithium-ion batteries,” npj Computational Materials, vol. 4, no. 1, 2018.[4] L. von Kolzenberg, J. Stadler, J. Fath, M. Ecker, B. Horstmann, and A. Latz, “A four parameter model for the solid-electrolyte interphase to predict battery aging during operation,” J. Power Sources, vol. 539, p. 231560, Aug. 2022.[5] P. M. Attia, S. J. Harris, and W. C. Chueh, “Benefits of fast battery formation in a model system,” J. Electrochem. Soc., vol. 168, no. 5, p. 050543, 2021.[6] P. Mohtat, S. Lee, J. B. Siegel, and A. G. Stefanopoulou, “Towards better estimability of electrode-specific state of health: Decoding the cell expansion,” J. Power Sources, vol. 427, pp. 101–111, July 2019. Figure 1

Representative grain boundaries during anisotropic grain growth

Conventional grain growth models do not account for the variability in grain boundary (GB) mobility, GB energy, and solute segregation energy that depend in detail on the GB structure. Instead, these parameters are typically determined empirically from experimental measurements. In this study, we present a systematic quantitative analysis that accounts for anisotropic GB properties, i.e., GB mobility and solute drag pressure to rationalize the average grain size evolution using representative GB properties under normal grain growth conditions in a non–textured system. We perform two–dimensional phase field simulations to analyze the role of (1) anisotropic mobility, (2) anisotropic segregation, and (3) combined anisotropic mobility and segregation on the average grain size evolution. A corresponding “representative GB” is introduced for each case considering a phenomenological grain growth model that fits the simulated average grain size evolution. A relationship is proposed to determine the representative GB properties for an arbitrary distribution of anisotropic GB properties in the initial microstructure. Simulations with the combined variation of GB mobility and segregation energy suggest that the representative GB mobility and segregation energy determined from independent simulations with varying either GB mobility or segregation energy can be superimposed to determine the average grain size evolution in agreement with the phase field simulations. The limits of validity, i.e., the range of moderate anisotropies, are identified where the phenomenological model with representative GB properties may be applicable, i.e., as long as a mean grain size is an appropriate descriptor of the grain structure.

Discrete Gompertz and Generalized Logistic models for early monitoring of the COVID-19 pandemic in Cuba

The COVID-19 pandemic has motivated a resurgence in the use of phenomenological growth models for predicting the early dynamics of infectious diseases. These models assume that time is a continuous variable, whereas in the present contribution the discrete versions of Gompertz and Generalized Logistic models are used for early monitoring and short-term forecasting of the spread of an epidemic in a region. The time-continuous models are represented mathematically by first-order differential equations, while their discrete versions are represented by first-order difference equations that involve parameters that should be estimated prior to forecasting. The methodology for estimating such parameters is described in detail. Real data of COVID-19 infection in Cuba is used to illustrate this methodology. The proposed methodology was implemented for the first thirty-five days and was used to predict accurately the data reported for the following twenty days.

An experimental study of morphological formation in bilayered tubular structures driven by swelling/growth

Circumferential wrinkling in soft tubular tissues is vital in supporting normal physiological functions. Most existing literature was dedicated to theoretical modeling and finite element simulations based on a specific growth model. This paper presents an experimental investigation on pattern formation and evolution in bilayered tubular organs using swelling deformation of polydimethylsiloxane (PDMS) and aims at supplying a thorough comparison with theoretical and finite element results. To create a twin model in modeling and simulation, the shear modulus in the incompressible neo-Hookean material is estimated via uni-axial tensile and pure shear tests. Five bilayered tubes with different material or geometrical parameters are fabricated. Swelling experiments are carried out for these samples in an individual experimental setup where a plane-strain deformation is guaranteed, and several surface patterns and the associated mode transformations are observed, namely, creases, wrinkles, period-doubling profiles, wrinkle-to-crease transition, and wrinkle-to-period-doubling transition. In particular, an interfacial wrinkling pattern is also observed. To make comparisons, a buckling analysis is conducted within the framework of finite elasticity by means of the Stroh formulation and a refined surface impedance matrix method. In addition, a finite element analysis (FEA) is performed to trace the evolution of surface instabilities. It turns out that the experimental findings agree well with the theoretical predictions as well as the finite element results. From our experiments, it is found that creasing mode may appear instead of wrinkling mode when both layers share a similar mechanical property. It is expected that the current work could provide novel experimental insight into pattern formation in tubular structures. In particular, the traditional impedance matrix method has been adapted, which enables us to resolve eigenvalue problems with displacement boundary conditions, and the good agreement among experimental, theoretical, and simulation consequences supplies strong evidence that a phenomenological growth model is satisfactory to reveal mechanisms behind intricate surface morphology in tubular tissues.

Orchestrated neuronal migration and cortical folding: A computational and experimental study.

Brain development involves precisely orchestrated genetic, biochemical, and mechanical events. At the cellular level, neuronal proliferation in the innermost zone of the brain followed by migration towards the outermost layer results in a rapid increase in brain surface area, outpacing the volumetric growth of the brain, and forming the highly folded cortex. This work aims to provide mechanistic insights into the process of brain development and cortical folding using a biomechanical model that couples cell division and migration with volumetric growth. Unlike phenomenological growth models, our model tracks the spatio-temporal development of cohorts of neurons born at different times, with each cohort modeled separately as an advection-diffusion process and the total cell density determining the extent of volume growth. We numerically implement our model in Abaqus/Standard (2020) by writing user-defined element (UEL) subroutines. For model calibration, we apply in utero electroporation (IUE) to ferret brains to visualize and track cohorts of neurons born at different stages of embryonic development. Our calibrated simulations of cortical folding align qualitatively with the ferret experiments. We have made our experimental data and finite-element implementation available online to offer other researchers a modeling platform for future study of neurological disorders associated with atypical neurodevelopment and cortical malformations.

Transmission Dynamics and Short-Term Forecasts of COVID-19: Nepal 2020/2021.

Nepal was hard hit by a second wave of COVID-19 from April-May 2021. We investigated the transmission dynamics of COVID-19 at the national and provincial levels by using data on laboratory-confirmed RT-PCR positive cases from the official national situation reports. We performed 8 week-to-week sequential forecasts of 10-days and 20-days at national level using three dynamic phenomenological growth models from 5 March 2021-22 May 2021. We also estimated effective and instantaneous reproduction numbers at national and provincial levels using established methods and evaluated the mobility trends using Google's mobility data. Our forecast estimates indicated a declining trend of COVID-19 cases in Nepal as of June 2021. Sub-epidemic and Richards models provided reasonable short-term projections of COVID-19 cases based on standard performance metrics. There was a linear pattern in the trajectory of COVID-19 incidence during the first wave (deceleration of growth parameter (p) = 0.41-0.43, reproduction number (Rt) at 1.1 (95% CI: 1.1, 1.2)), and a sub-exponential growth pattern in the second wave (p = 0.61 (95% CI: 0.58, 0.64)) and Rt at 1.3 (95% CI: 1.3, 1.3)). Across provinces, Rt ranged from 1.2 to 1.5 during the early growth phase of the second wave. The instantaneous Rt fluctuated around 1.0 since January 2021 indicating well sustained transmission. The peak in mobility across different areas coincided with an increasing incidence trend of COVID-19. In conclusion, we found that the sub-epidemic and Richards models yielded reasonable short-terms projections of the COVID-19 trajectory in Nepal, which are useful for healthcare utilization planning.

Modeling low and high temperature controls in the growth of graphene-CNT hybrids by PECVD: an interplay between process and plasma parameters

The effect of process parameters such as the pressure, power, and substrate bias on the dimensions of CNT, graphene, and graphene-CNT hybrids in the low and high temperature regime is described by a multispecies plasma-assisted and catalyst-aided phenomenological growth model of graphene-carbon nanotube (CNT) hybrids. An interplay established in the present work between the process and plasma parameters (such as the electron density and temperature, and radical flux) characterizes the process parameters effects. It is found that this interplay is remarkably different at low and high temperature owing to the different processes that dominate during the growth in these temperature regimes.

Mid-Epidemic Forecasts of COVID-19 Cases and Deaths: A Bivariate Model Applied to the UK.

Background The evolution of the COVID-19 epidemic has been accompanied by efforts to provide comparable international data on new cases and deaths. There is also accumulating evidence on the epidemiological parameters underlying COVID-19. Hence, there is potential for epidemic models providing mid-term forecasts of the epidemic trajectory using such information. The effectiveness of lockdown or lockdown relaxation can also be assessed by modelling later epidemic stages, possibly using a multiphase epidemic model. Methods Commonly applied methods to analyse epidemic trajectories or make forecasts include phenomenological growth models (e.g., the Richards family of densities) and variants of the susceptible-infected-recovered (SIR) compartment model. Here, we focus on a practical forecasting approach, applied to interim UK COVID data, using a bivariate Reynolds model (for cases and deaths), with implementation based on Bayesian inference. We show the utility of informative priors in developing and estimating the model and compare error densities (Poisson-gamma, Poisson-lognormal, and Poisson-log-Student) for overdispersed data on new cases and deaths. We use cross validation to assess medium-term forecasts. We also consider the longer-term postlockdown epidemic profile to assess epidemic containment, using a two-phase model. Results Fit to interim mid-epidemic data show better fit to training data and better cross-validation performance for a Poisson-log-Student model. Estimation of longer-term epidemic data after lockdown relaxation, characterised by protracted slow downturn and then upturn in cases, casts doubt on effective containment. Conclusions Many applications of phenomenological models have been to complete epidemics. However, evaluation of such models based simply on their fit to observed data may give only a partial picture, and cross validation against actual trends is also valuable. Similarly, it may be preferable to model incidence rather than cumulative data, although this raises questions about suitable error densities for modelling often erratic fluctuations. Hence, there may be utility in evaluating alternative error assumptions.

Measuring differences between phenomenological growth models applied to epidemiology

Phenomenological growth models (PGMs) provide a framework for characterizing epidemic trajectories, estimating key transmission parameters, gaining insight into the contribution of various transmission pathways, and providing long-term and short-term forecasts. Such models only require a small number of parameters to describe epidemic growth patterns. They can be expressed by an ordinary differential equation (ODE) of the type C′(t)=f(t,C;Θ) for t>0, C(0)=C0, where t is time, C(t) is the total size of the epidemic (the cumulative number of cases) at time t, C0 is the initial number of cases, f is a model-specific incidence function, and Θ is a vector of parameters. The current COVID-19 pandemic is a scenario for which such models are of obvious importance. In Bürger et al. (2019) it is demonstrated that some PGMs are better at fitting data of specific epidemic outbreaks than others even when the models have the same number of parameters. This situation motivates the need to measure differences in the dynamics that two different models are capable of generating. The present work contributes to a systematic study of differences between PGMs and how these may explain the ability of certain models to provide a better fit to data than others. To this end a so-called empirical directed distance (EDD) is defined to describe the differences in the dynamics between different dynamic models. The EDD of one PGM from another one quantifies how well the former fits data generated by the latter. The concept of EDD is, however, not symmetric in the usual sense of metric spaces. The procedure of calculating EDDs is applied to synthetic data and real data from influenza, Ebola, and COVID-19 outbreaks.

Comparison of phenomenological growth models in predicting cumulative number of COVID-19 cases in East Java Province, Indonesia

In this paper, five phenomenological (Richards, a generalized Richards, Blumberg, Tsoularis & Wallace, and Gompertz) models are implemented to predict the cumulative number of COVID-19 cases. The five phenomenological models are in the form of ordinary differential equations with a few number of model parameters. The model parameters of each model were calibrated by fitting the model with the reported cumulative number of COVID-19 cases in East Java Province from March 25 until October 31, 2020 via nonlinear least square method. We compare the performance of the five phenomenological models by measuring four performance metrics, namely the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of determination (R2) and the Akaike information criterion (AIC). When calibrating the cumulative number of cases, the five models perform very well, which are indicated by their high coefficient of determination (R2>0.999). However, a comparison of the four- performance metrics shows that Tsoularis & Wallace performed the best followed by a generalized Richards model. The prediction for the final size of the COVID-19 epidemic in East Java according to the Tsoularis & Wallace model is K=78 002. Both Richards and Gompertz models tend to underestimate the final size of the epidemic, while the Blumberg model tends to overestimate. The five models estimate the peak of the COVID-19 epidemic in East Java has been occurred on August 13-14, 2020. Using the predicted cumulative number of cases, we determine the daily new cases of COVID-19 in East Java. Based on the four-performance metrics, it appears that the five phenomenological models predict new daily cases of COVID-19 equally well.

Crack-growth controlled failure of short fibre reinforced thermoplastics: Influence of fibre orientation

The effect of flow-induced fibre orientation on the fatigue performance of short fibre reinforced thermoplastics is investigated. Relative contributions of creep (static, time-dependent) and fatigue (cycle dependent) components are studied extensively by performing tests at different frequencies and load ratios for different fibre orientations and fibre weight fractions. An anisotropic, phenomenological model of crack growth controlled failure is proposed that relates creep/fatigue contributions to the lifetime in the crack growth controlled failure region for different fibre orientations and allows to extrapolate and estimate time-to-failure under a static load using short-term cyclic tests.

Outbreak analysis with a logistic growth model shows COVID-19 suppression dynamics in China.

China reported a major outbreak of a novel coronavirus, SARS-CoV2, from mid-January till mid-March 2020. We review the epidemic virus growth and decline curves in China using a phenomenological logistic growth model to summarize the outbreak dynamics using three parameters that characterize the epidemic's timing, rate and peak. During the initial phase, the number of virus cases doubled every 2.7 days (range 2.2-4.4 across provinces). The rate of increase in the number of reported cases peaked approximately 10 days after suppression measures were started on 23-25 January 2020. The peak in the number of reported sick cases occurred on average 18 days after the start of suppression measures. From the time of starting measures till the peak, the number of cases increased by a factor 39 in the province Hubei, and by a factor 9.5 for all of China (range: 6.2-20.4 in the other provinces). Complete suppression took up to 2 months (range: 23-57d.), during which period severe restrictions, social distancing measures, testing and isolation of cases were in place. The suppression of the disease in China has been successful, demonstrating that suppression is a viable strategy to contain SARS-CoV2.

A novel sub-epidemic modeling framework for short-term forecasting epidemic waves

BackgroundSimple phenomenological growth models can be useful for estimating transmission parameters and forecasting epidemic trajectories. However, most existing phenomenological growth models only support single-peak outbreak dynamics whereas real epidemics often display more complex transmission trajectories.MethodsWe develop and apply a novel sub-epidemic modeling framework that supports a diversity of epidemic trajectories including stable incidence patterns with sustained or damped oscillations to better understand and forecast epidemic outbreaks. We describe how to forecast an epidemic based on the premise that the observed coarse-scale incidence can be decomposed into overlapping sub-epidemics at finer scales. We evaluate our modeling framework using three outbreak datasets: Severe Acute Respiratory Syndrome (SARS) in Singapore, plague in Madagascar, and the ongoing Ebola outbreak in the Democratic Republic of Congo (DRC) and four performance metrics.ResultsThe sub-epidemic wave model outperforms simpler growth models in short-term forecasts based on performance metrics that account for the uncertainty of the predictions namely the mean interval score (MIS) and the coverage of the 95% prediction interval. For example, we demonstrate how the sub-epidemic wave model successfully captures the 2-peak pattern of the SARS outbreak in Singapore. Moreover, in short-term sequential forecasts, the sub-epidemic model was able to forecast the second surge in case incidence for this outbreak, which was not possible using the simple growth models. Furthermore, our findings support the view that the national incidence curve of the Ebola epidemic in DRC follows a stable incidence pattern with periodic behavior that can be decomposed into overlapping sub-epidemics.ConclusionsOur findings highlight how overlapping sub-epidemics can capture complex epidemic dynamics, including oscillatory behavior in the trajectory of the epidemic wave. This observation has significant implications for interpreting apparent noise in incidence data where the oscillations could be dismissed as a result of overdispersion, rather than an intrinsic part of the epidemic dynamics. Unless the oscillations are appropriately modeled, they could also give a false positive, or negative, impression of the impact from public health interventions. These preliminary results using sub-epidemic models can help guide future efforts to better understand the heterogenous spatial and social factors shaping sub-epidemic patterns for other infectious diseases.

Multiscale crystal-plasticity phase field and extended finite element methods for fatigue crack initiation and propagation modeling

This paper presents a physics-based prediction of crack initiation at the microstructure level using the phase field (PF) model without finite element discretization, coupled with an efficient and accurate modeling of crack propagation at macro-scale based on extended finite element method (XFEM). Although the macro-scale model assumes linear elastic material behavior, at micro-scale the behavior of plastically deforming heterogeneous polycrystals is taken into account by coupling the PF model and a crystal plasticity model in the fast Fourier transform computational framework. A sequential coupling has been established for the multiscale modeling where the macro-scale finite element (FE) model determines the hot spots at each cyclic loading increment and passes the associated stress/strain values to the unit-cell phase-field model for accurate physics-based microstructure characterization and prediction of plasticity induced crack initiation. The PF model predicts the number of cycles for the crack initiation and the phenomenological crack growth models are employed to propagate the initiated crack by the appropriate length to be inserted in the FE mesh. Finally, the XFEM solution module is activated to perform mesh independent crack propagation from its initial crack size to the final size for the total life prediction. The effectiveness of the proposed multiscale method is demonstrated through numerical examples.

Kinetics during endotaxial growth of CoSi2 nanowires and islands on Si(0 0 1)

We propose a phenomenological growth model describing the morphological evolution of two different (ridge and flat) types of endotaxial CoSi2 islands as a function of growth temperature from 500 °C to 800 °C and for Cobalt coverages from 0.1 monolayer (ML) to 0.5ML. The presence of low energy Type A and Type B CoSi2{1 1 1}-Si{1 1 1} interfaces drives the formation of flat-type islands and ridge-type nanowires respectively. The growth of these nanowires and islands are kinetically constrained, where the islands’ length, width and height are experimentally found to follow the Arrhenius relation with activation energies ranging between 0.4 eV and 1.6 eV. Our model suggests that the islands are kinetically constrained by thermally-activated processes such as island-edge diffusion anisotropy and corner energy-barriers, thereby restricting the adatom transfer between long and short sides of the islands. Consequently, at low growth temperatures, ridge-type nanowires are more dot-like while flat-type islands form small wire-like islands. But at high growth temperatures, the ridge islands form long nanowires while the flat islands become more dot-like instead.

Interactive effects of cyclic oxidation and structural evolution for Ti-6Al-4V/(TiC+TiB) alloy composites at elevated temperatures

A kind of Ti-6Al-4V alloy matrix composite with coupled (TiC+TiB) networks as reinforcements was conceived and actually prepared by reaction hot pressing technique. Its internal microstructures transferred from Widmanstätten lamellae into equiaxed α-Ti grains during in-situ synthesizing reactions, which were characterized by HRTEM analyses to reveal the crystallographic correlations. With an effort to enhance its high-temperature oxidation resistance, the cyclic oxidation kinetics and concomitant structural evolution were experimentally investigated and thermodynamically elucidated in the 873–1073 K temperature range. The specially designed network configuration of hybrid reinforcers was found to improve the oxidation resistance to a remarkable extent. The cyclic oxidation kinetics followed the classic parabolic relation at the relatively lower temperature of 873 K, but this was replaced by a linear trend once temperature rose up to 1073 K. It was revealed that the thermal-stress induced spallation of oxide scales was the dominant factor to modulate the interaction of oxidation kinetics and structural evolution. A phenomenological model of oxide scale growth was proposed accordingly to depict the kinetics transition of cyclic oxidation process.