Applied Mathematical Modelling

Volume 38
M. Twarogowska | P. Goatin | R. Duvigneau

Editors’ motivation for choosing this article
This paper deals with crowd dynamics in the context of macroscopic modelling of evacuation of pedestrians from a room through a narrow exit. It numerically investigates two models, which are the Hughes model and the Payne–Whitham vehicular traffic model. Understanding crowd dynamics is valuable in situations that are life-threatening (wars, earthquakes, hurricanes, virus outbreak, etc.) where nervousness and panic force a crowd to move faster without following optimal routes. The results of the numerical experiments show that Hughes model cannot reproduce stop-and-go waves in traffic flow or clogging at bottlenecks. The numerical results verified that a second order model captures better the structure of interactions between pedestrians.

Volume 38
B. De Filippo | F. Clarelli | R. Natalini

Editors’ motivation for choosing this article
The authors give a good introductory background to the problem of tarnishing copper and bronze artifacts in SO2 -enriched urban atmospheres. This is a recognized practical problem, with broad public interest. They then set up a mathematical model involving diffusion of SO2 and swelling of a tarnish layer with two free boundaries. The model is based on sound chemical and physical principles. The mass transport problem is simple and understandable, yet it leads to an intrinsically interesting free boundary problem. Numerical solutions show very good agreement with laboratory data, after which actual atmospheric data are used to calibrate the model so that predictions can be made to the response to changes in atmospheric composition and temp

Volume 38
Akio Tomiyama | Motoki Irikura | Munenori Maekawa | Shigeo Hosokawa

Editors’ motivation for choosing this article
The selected paper addresses a fluid mechanics problem of industrial importance. The choice of numerical model was motivated by the possibility of simulating slugging on a computational grid of practical size for modelling in industry. The model was validated against experimental results. Prediction of slugging was found to be sufficiently accurate to use the model as a design tool. Importantly, the model predictions were used to help understand the physical mechanisms of slugging.