Structural Efficiency of Percolated Landscapes in Flow Networks

The large-scale structure of complex systems is intimately related to their functionality and evolution. In particular, global transport processes in flow networks rely on the presence of directed pathways from input to output nodes and edges, which organize in macroscopic connected components. However, the precise relation between such structures and functional or evolutionary aspects remains to be understood. Here, we investigate which are the constraints that the global structure of directed networks imposes on transport phenomena. We define quantitatively under minimal assumptions the structural efficiency of networks to determine how robust communication between the core and the peripheral components through interface edges could be. Furthermore, we assess that optimal topologies in terms of access to the core should look like "hairy balls'' so to minimize bottleneck effects and the sensitivity to failures. We illustrate our investigation with the analysis of three real networks with very different purposes and shaped by very different dynamics and time scales-the Internet customer provider set of relationships, the nervous system of the worm Caenorhabditis elegans, and the metabolism of the bacterium Escherichia coli. Our findings prove that different global connectivity structures result in different levels of structural efficiency. In particular, biological networks seem to be close to the optimal layout.

Numerical characterization and engineering of transport in morphologically complex heterogeneous media

Xiaoyu Dai

A multi-scale numerical methodology for the assessment of radiation and optical characteristics of complex structured soot-contaminated snow layers was investigated first. The methodology accounted for the exact morphology at the various scales and utilizes volume-averaging approaches with the corresponding effective properties to couple the scales. At the continuum level, the volume-averaged coupled radiative transfer equations were solved utilizing i) effective radiative transport properties obtained by direct Monte Carlo simulations at the pore level, and ii) averaged bulk material properties obtained at particle level by discrete dipole approximation calculations. The contribution of soot additives to the radiative forcing was quantitatively estimated by numerical simulation and qualitatively validated with the published experimental data.Additional coupled heat and mass transfer phenomena were then investigated for a two-step solar thermochemical water/carbon dioxide splitting reactor. It was composed of two distinct scales: porous reacting materials at the mesoscale and a batch reactor at the macro-scale. A transient multi-physics volume-averaged model of the reactive porous media undergoing the reduction and oxidation steps was developed. The effective heat and mass transport properties of reticulated porous foams were incorporated through porosity-dependent empirical correlations. Porosity-dependent reduction, oxidation, and cyclic performance for a uniform and homogenous porous structure were assessed and followed by the investigation of diverse structures with non-uniform porosities along the reactor. Subsequently, the effect of structural anisotropy on the system performance was assessed by extending the previous model into 2-dimensions. The porous medium was assumed to exhibit anisotropic transport behaviors in terms of heat transfer (radiation, conduction, convection) and mass transfer. Additionally, two operational configurations were investigated: a conventional concurrent flow configuration of fluid and irradiation and a scenario where the principal flow axis was perpendicular to the irradiation direction. In terms of radiative properties, a structure with a complete forward scattering phase function and low scattering albedo ensured the largest absorption, increasing the production rate. Anisotropic structures with a higher degree of anisotropy in permeability were more favored when the incoming radiation was perpendicular to the fluid flow direction, where the interphase heat convection was enhanced.Lastly, the engineering of the porous structure was explored by establishing a direct relationship between the local morphological characteristics and the reduction performance. This was implemented by direct-pore simulations on the discrete scale that were directly coupled to the volume-averaged finite volume simulations on the continuum scale. A large number of porous structures were artificially generated and its transport characteristics calculated by the pore-levels simulations. These calculated results were used to train a machine-learning algorithm that predicted the oxygen yield solely from based on the morphology. The learning algorithm identified the most significant morphological descriptors for a specific performance target and provided guidelines for the optimal porous structure design.

EPFL2021

Numerical characterization and engineering of transport in morphologically complex heterogeneous media

Xiaoyu Dai

EPFL2021