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A high fidelity model for the propagation of pathogens via aerosols in the presence of moving pedestrians is proposed. The key idea is the tight coupling of computational fluid dynamics and computational crowd dynamics in order to capture the emission, transport and inhalation of pathogen loads in space and time. An example simulating pathogen propagation in a narrow corridor with moving pedestrians clearly shows the considerable effect that pedestrian motion has on airflow, and hence on pathogen propagation and potential infectivity.

 

We consider an optimal control problem where the state equations are a coupled hyperbolic–elliptic system. This system arises in elastodynamics with piezoelectric effects—the elastic stress tensor is a function of elastic displacement and electric potential. The electric flux acts as the control variable and bound constraints on the control are considered. We develop a complete analysis for the state equations and the control problem. The requisite regularity on the control, to show the well-posedness of the state equations, is enforced using the cost functional. We rigorously derive the first-order necessary and sufficient conditions using adjoint equations and further study their well-posedness. For spatially discrete (time-continuous) problems, we show the convergence of our numerical scheme. Three-dimensional numerical experiments are provided showing convergence properties of a fully discrete method and the practical applicability of our approach.

 

Purpose The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour. Design/methodology/approach A series of runs were conducted for a canonical test problem. These were used as databases or “learning sets” for both interpolation algorithms and deep neural networks. A second set of runs was conducted to test the prediction accuracy of both approaches. Findings The results indicate that interpolation algorithms outperform deep neural networks in accuracy for linear heat conduction, while the reverse is true for nonlinear heat conduction problems. For heat convection problems, both methods offer similar levels of accuracy. Originality/value This is the first time such a comparison has been made.