Using a Bayesian approach to epidemiological compartmental modeling, we demonstrate the "bomb-like" behavior of exponential growth in COVID-19 cases can be explained by transmission of asymptomatic and mild cases that are typically unreported at the beginning of pandemic events due to lower prevalence of testing. We studied the exponential phase of the pandemic in Italy, Spain, and South Korea, and found the R0 to be 2.56 (95% CrI, 2.41-2.71), 3.23 (95% CrI, 3.06-3.4), and 2.36 (95% CrI, 2.22-2.5) if we use Bayesian priors that assume a large portion of cases are not detected. Weaker priors regarding the detection rate resulted in R0 values of 9.22 (95% CrI, 9.01-9.43), 9.14 (95% CrI, 8.99-9.29), and 8.06 (95% CrI, 7.82-8.3) and assumes nearly 90% of infected patients are identified. Given the mounting evidence that potentially large fractions of the population are asymptomatic, the weaker priors that generate the high R0 values to fit the data required assumptions about the epidemiology of COVID-19 that do not fit with the biology, particularly regarding the timeframe that people remain infectious. Our results suggest that models of transmission assuming a relatively lower R0 value that do not consider a large number of asymptomatic cases can result in misunderstanding of the underlying dynamics, leading to poor policy decisions and outcomes.
A micromechanical multi-physics model for ceramics has been recalibrated and used to simulate impact experiments with boron carbide in ABAQUS. The dominant physical mechanisms in boron carbide have been identified and simulated in the framework of an integrated constitutive model that combines crack growth, amorphization and granular flow. The integrative model is able to accurately reproduce some of the key cracking patterns of Sphere Indentation experiments and Edge On Impact experiments. Based on this integrative model, linear regression has been used to study the sensitivity of sphere indentation model predictions to the input parameters. The sensitivities are connected to physical mechanisms, and trends in model outputs have been intuitively explored. These results help suggest material modifications that might improve material performance, prioritize calibration experiments for materials-by-design iterations, and identify model parameters that require more in-depth understanding.
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic collocation method with adaptive mesh refinement (SCAMR) to deal with high dimensional stochastic systems with discontinuities. Specifically, the proposed approach uses generalized polynomial chaos (gPC) expansion with Legendre polynomial basis and solves for the gPC coefficients using the least squares method. It also implements an adaptive mesh (element) refinement strategy which checks for abrupt variations in the output based on the second order gPC approximation error to track discontinuities or non-smoothness. In addition, the proposed method involves a criterion for checking possible dimensionality reduction and consequently, the decomposition of the full-dimensional problem to a number of lower-dimensional subproblems. Specifically, this criterion checks all the existing interactions between input dimensions of a specific problem based on the high-dimensional model representation (HDMR) method, and therefore automatically provides the subproblems which only involve interacting dimensions. The efficiency of the approach is demonstrated using both smooth and non-smooth function examples with input dimensions up to 300, and the 1 Corresponding author.approach is compared against other existing algorithms.
Stochastic microstructure reconstruction involves digital generation of microstructures that match key statistics and characteristics of a (set of) target microstructure(s). This process enables computational analyses on ensembles of microstructures without having to perform exhaustive and costly experimental characterizations. Statistical functions-based and deep learning-based methods are among the stochastic microstructure reconstruction approaches applicable to a wide range of material systems. In this paper, we integrate statistical descriptors as well as feature maps from a pre-trained deep neural network into an overall loss function for an optimization based reconstruction procedure. This helps us to achieve significant computational efficiency in reconstructing microstructures that retain the critically important physical properties of the target microstructure. A numerical example for the microstructure reconstruction of bi-phase random porous ceramic material demonstrates the efficiency of the proposed methodology. We further perform a detailed finite element analysis (FEA) of the reconstructed microstructures to calculate effective elastic modulus, effective thermal conductivity and effective hydraulic conductivity, in order to analyse the algorithm's capacity to capture the variability of these material properties with respect to those of the target microstructure. This method provides an economic, efficient and easy-to-use approach for reconstructing random multiphase materials in 2D which has potential to be extended to 3D structures.
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