Modeling micro-macro pedestrian counterflow in heterogeneous domains

We present a micro-macro strategy able to describe the dynamics of crowds in heterogeneous media. Herein we focus on the example of pedestrian counterflow. The main working tools include the use of mass and porosity measures together with their transport as well as suitable application of a version of Radon-Nikodym Theorem formulated for finite measures. Finally, we illustrate numerically our microscopic model and emphasize the effects produced by an implicitly defined social velocity. Keywords: Crowd dynamics; mass measures; porosity measure; social network

The effect of perception anisotropy on particle systems describing pedestrian flows in corridors

We consider a microscopic model (a system of self-propelled particles) to study the behaviour of a large group of pedestrians walking in a corridor. Our point of interest is the effect of anisotropic interactions on the global behaviour of the crowd. The anisotropy we have in mind reflects the fact that people do not perceive (i.e. see, hear, feel or smell) their environment equally well in all directions. The dynamics of the individuals in our model follow from a system of Newton-like equations in the overdamped limit. The instantaneous velocity is modelled in such a way that it accounts for the angle under which an individual perceives another individual. We investigate the effects of this perception anisotropy by means of simulations, very much in the spirit of molecular dynamics. We define a number of characteristic quantifiers (including the polarization index and Morisita index) that serve as measures for e.g. organization and clustering, and we use these indices to investigate the influence of anisotropy on the global behaviour of the crowd. The goal of the paper is to investigate the potentiality of this model; extensive statistical analysis of simulation data, or reproducing any specific real-life situation are beyond its scope.Comment: 24 page

Crowds reaching targets by maximizing entropy: a Clausius-Duhem inequality approach

In this paper we propose the use of concepts from thermodynamics in the study of crowd dynamics. Our continuous model consists of the continuity equation for the density of the crowd and a kinetic equation for the velocity field. The latter includes a nonlocal term that models interactions between individuals. To support our modelling assumptions, we introduce an inequality that resembles the Second Law of Thermodynamics, containing an entropy-like functional. We show that its time derivative equals a positive dissipation term minus a corrector term. The latter term should be small for the time derivative of the entropy to be positive. In case of isotropic interactions the corrector term is absent. For the anisotropic case, we support the claim that the corrector term is small by simulations for the corresponding particle system. They reveal that this term is sufficiently small for the entropy still to increase. Moreover, we show that the entropy converges in time towards a limit value

Modelling with measures: Approximation of a mass-emitting object by a point source

We consider a linear diffusion equation on $\Omega:=\mathbb{R}^2\setminus\bar{\Omega_\mathcal{O}}$, where $\Omega_\mathcal{O}$ is a bounded domain. The time-dependent flux on the boundary $\Gamma:=\partial\Omega_\mathcal{O}$ is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of $\mathbb{R}^2$ with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time $t$, we derive an $L^2([0,t];L^2(\Gamma))$-bound on the difference in flux on the boundary. Moreover, we derive for all $t>0$ an $L^2(\Omega)$-bound and an $L^2([0,t];H^1(\Omega))$-bound for the difference of the solutions to the two models

The influence of social factors on gender health

Male births exceed female births by 5-6% (for a sex ratio at birth of 1.05-1.06) while a women's life expectancy, on a global scale, is about 6 years longer. Thus within various age groups the male:female ratio changes over time. Until age 50 years men outnumber women; thereafter their numbers show a sharp decline. Consequently at age 80 years, there are many more women than men. An estimated 25% of this male excess mortality is due to biological causes, the rest being explained by behavioural, cultural and environmental factors. For both women and men, the main health risks related to lifestyle are smoking, alcohol, unhealthy diet and physical inactivity. In the year 2010, overweight (BMI: 25-29 kg/m2) and obesity (BMI: >30 kg/m2) were responsible for over 3 million deaths, with similar relative risks in men and women for overweight and obesity. Smoking and alcohol are the major causes of the global gender gap in mortality. For women in some parts of the world however pregnancy is also hazardous. On a global scale, in 2013 about 300 000 deaths were related to pregnancy, with sub-Saharan Africa registering the highest maternal mortality: over 500 maternal deaths per 100 000 births. Additional woman's health risks arise from gender discrimination, including sex-selective abortion, violence against women and early child marriage. Providers should be aware of the effect that these risks can have on both reproductive and general health. © 2016 The Author

Pattern formation in a two-species aggregation model

We consider a system of two aggregation equations. This system consists of two continuity equations for the densities $\rho_1$ and $\rho_2$, coupled via the the velocities $v_1$ and $v_2$. Each $v_i$ is given by $v_i = -\nabla K_{ii} * \rho_i -\nabla K_{ij} * \rho_j$, where the former convolution term accounts for self-interactions and the latter one for cross-interactions. Each kernel is chosen such that the interactions exhibit Newtonian repulsion and linear attraction (i.e., the kernel is quadratic). The free parameters in the model are the coefficients multiplying the repulsion and attraction parts. We assume that the interactions are symmetric, in the sense that $K_{11}=K_{22}$ and $K_{12}=K_{21}$. Our aim is to characterise the steady states of the model and their stability for varying model parameters. For our specific interaction kernels, it is known that the density can take only two different values in a steady state, depending on whether the two densities coexist at a certain position or not. However, the geometry of the supports of $\rho_1$ and $\rho_2$ is far from trivial.Non UBCUnreviewedAuthor affiliation: Simon Fraser University and Dalhousie UniversityPostdoctora