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The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
Understanding processes in porous media is fundamental to a broad spectrum of environmental, energy, and geoscience applications. These processes include multiphase fluid transport, interfacial dynamics, reactive transformations, and…
Fluid flow through bimodal porous media, characterized by a distinct separation in pore size distribution, is critical in various scientific and engineering applications, including groundwater management, oil and gas production, and carbon…
A poromechanical model of partially saturated deformable porous media is proposed based on a phase field approach at modeling the behavior of the mixture of liquid water and wet air, which saturates the pore space, the phase field being the…
Knowledge of the underlying mechanisms of multiphase flow dynamics in porous media is crucial for optimizing subsurface engineering applications like geological carbon sequestration. However, studying the micro-mechanisms of multiphase…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
Multicomponent multiphase reactive transport processes with dissolution-precipitation are widely encountered in energy and environment systems. A pore-scale two-phase multi-mixture model based on the lattice Boltzmann method (LBM) is…
We consider a new model for complex networks whose underlying mechanism is extending dense subgraphs. In the frustum model, we iteratively extend cliques over discrete-time steps. For many choices of the underlying parameters, graphs…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
We present a new model for two phase Darcy flows in fractured media, in which fractures are modelled as submanifolds of codimension one with respect to the surrounding domain (matrix). Fractures can act as drains or as barriers, since…
The network of interactions among fluid elements and coherent structures gives rise to the incredibly rich dynamics of vortical flows. These interactions can be described with the use of mathematical tools from the emerging field of network…
A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels using an optical technique allowing for simultaneous local and global…
The objective of this study is to highlight the effect of porosity variation in a topology optimization process in the field of fluid dynamics. Usually a penalization term added to momentum equation provides to get material distribution.…