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The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…

The simulation of fluid flow in real, multiscale porous media remains challenging due to the complexity of nanoscale phenomena and the difficulty of developing upscaling methodologies. In this study, we introduce a multiscale filtration…

Pore-scale observation of vortical flow structures in porous media is a significant challenge in many natural and industrial systems. Vortical structure dynamics is believed to be the driving mechanism in the transition regime in porous…

Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…

We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input…

In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum…

Topological phase transitions can be described by the theory of critical phenomena and identified by critical exponents that define their universality classes. This is a consequence of the existence of a diverging length at the transition…

Topological states enable robust transport within disorder-rich media through integer invariants inextricably tied to the transmission of light, sound, or electrons. However, the challenge remains to exploit topological protection in a…

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…

It is widely recognized that the structure of porous media is of relevance for a variety of mechanical and physical phenomena. The focus of the present work is on capillarity, a pore-scale process occurring at the micron scale. We attempt…

Recent studies have revealed the central role of chaotic stretching and folding at the pore scale in controlling mixing within porous media, whether the solid phase is discrete (as in granular and packed media) or continuous (as in vascular…

Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…

Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…

A pore-scale model is introduced for two-phase flow in dense packings of polydisperse spheres. The model is developed as a component of a more general hydromechanical coupling framework based on the discrete element method, which will be…

When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are…

In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…

The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…

Turbulent flows over porous lattices consisting of rectangular cuboid pores are investigated using scale-resolving direct numerical simulations. Beyond a certain threshold which is primarily determined by the wall-normal Darcy permeability,…