Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors.

The expansion of biological species in natural environments is usually described as the combined effect individual spatial dispersal and growth. In the case of aquatic ecosystems flow transport can also be extremely relevant as an extra, advection induced, dispersal factor. We designed and assembled a dedicated microfluidic device to control and quantify the expansion of populations of E. coli bacteria under both co-flowing and counter-flowing conditions, measuring the front speed at varying intensity of the imposed flow.

This paper investigates the problem of quantifying the impact of unex- pected deviations of mortality trend on a longevity indexed life annuity in a Solvency II perspective. Solvency II quantitative requirements regulate the margins required to offset the insurance risk in a one year risk horizon. Indeed, the idea of deepening the expected changes of future mortality rates over a single year is gaining. In the following the authors propose a com- putational tractable approach to assess the technical provisions by means of an internal model, in line with Solvency II directives.

The rapid development of cyber insurance market brings for- ward the question about the effect of cyber insurance on cyber security. Some researchers believe that the effect should be positive as organisa- tions will be forced to maintain a high level of security in order to pay lower premiums. On the other hand, other researchers conduct a theo- retical analysis and demonstrate that availability of cyber insurance may result in lower investments in security. In this paper we propose a mathematical analysis of a cyber-insurance model in a non-competitive market.

The numerical solution of reaction-diffusion systems modelling predator-prey dynamics using implicit-symplectic (IMSP) schemes is relatively new. When applied to problems with chaotic dynamics they perform well, both in terms of computational effort and accuracy. However, until the current paper, a rigorous numerical analysis was lacking. We analyse the semi-discrete in time approximations of a first-order IMSP scheme applied to spatially extended predator-prey systems.

We propose novel positive numerical integrators for approximating predator-prey models. The schemes are based on suitable symplectic procedures applied to the dynamical system written in terms of the log transformation of the original variables. Even if this approach is not new when dealing with Hamiltonian systems, it is of particular interest in population dynamics since the positivity of the approximation is ensured without any restriction on the temporal step size. When applied to separable M-systems, the resulting schemes are proved to be explicit, positive, Poisson maps.

By applying Helmholtz decomposition, the unknowns of a linearized Euler system can be recast as solutions of uncoupled linearwave equations. Accordingly, the Kirchhoff expression of the exact solutions is recast as a time-marching, Lax-Wendroff type, numerical scheme for which consistency with one-dimensional upwinding is checked. This discretization, involving spherical means, is set up on a 2D uniform Cartesian grid, so that the resulting numerical fluxes can be shown to be conservative.

We numerically study the behavior of self-propelled liquid droplets whose motion is triggered by a Marangoni-like flow. This latter is generated by variations of surfactant concentration which affect the droplet surface tension promoting its motion. In the present paper a model for droplets with a third amphiphilic component is adopted. The dynamics is described by Navier-Stokes and convection-diffusion equations, solved by the lattice Boltzmann method coupled with finite-difference schemes. We focus on two cases.