Coupling radiative, conductive and convective heat-transfers in a single Monte Carlo algorithm: A general theoretical framework for linear situations.

It was recently shown that radiation, conduction and convection can be combined within a single Monte Carlo algorithm and that such an algorithm immediately benefits from state-of-the-art computer-graphics advances when dealing with complex geometries. The theoretical foundations that make this coupling possible are fully exposed for the first time, supporting the intuitive pictures of continuous thermal paths that run through the different physics at work. First, the theoretical frameworks of propagators and Green's functions are used to demonstrate that a coupled model involving different physical phenomena can be probabilized. Second, they are extended and made operational using the Feynman-Kac theory and stochastic processes. Finally, the theoretical framework is supported by a new proposal for an approximation of coupled Brownian trajectories compatible with the algorithmic design required by ray-tracing acceleration techniques in highly refined geometry.

The interplay between a self-organized process and an environmental template: corpse clustering under the influence of air currents in ants.

Many spatial patterns observed in nature emerge from local processes and their interactions with the local environment. The clustering of objects by social insects represents such a pattern formation process that can be observed at both the individual and the collective level. In this paper, we study the interaction between air currents and clustering behaviour in order to address the coordinating mechanisms at the individual level that underlie the spatial pattern formation process in a heterogeneous environment. We choose the corpse clustering behaviour of the ant Messor sanctus as an experimental paradigm. In a specifically designed experimental set-up with a well-controlled laminar air flow (approx. 1 cm s-1), we first quantify the modulation of the individual corpse aggregation behaviour as a function of corpse density, air flow intensity and the ant's position with respect to corpse piles and air flow direction. We then explore by numerical simulation how the forming corpse piles modify the laminar air flow around them and link this result with the individual behaviour modulation. Finally, we demonstrate on the collective level that this laminar air flow leads to an elongation and a slow displacement of the formed corpse piles in the direction of the air current. Both the individual behaviour modulated by air flow and the air flow modulated by the forming corpse piles can explain the pile patterns observed on the collective level as a stigmergic process. We discuss the generality of this coordinating mechanism to explain the clustering phenomena in heterogeneous environments reported in the literature.