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Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…
We present a percolation model that is inspired by recent works on immiscible two-phase flow in a mixed-wet porous medium made of a mixture of grains with two different wettability properties. The percolation model is constructed on a dual…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
Pore-network modeling is a widely used predictive tool for pore-scale studies in various applications that deal with multiphase flow in porous media. Despite recent improvements to enable pore-network modeling on simplified pore geometry…
Understanding porous media properties and their scale dependence have been an active subject of research in the past several decades in hydrology, geosciences and petroleum engineering. The scale dependence of flow in porous media is…
Convective mixing in porous media is crucial in both geophysical and industrial fields, spanning applications ranging from carbon dioxide sequestration to contaminant transport in groundwater. Key processes are affected by convective heat…
Dissolution in porous media and fractured rocks alters both the chemical composition of the fluid and the physical properties of the solid. Depending on system conditions, reactive flow may enlarge pores uniformly, widen pre-existing…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
Topological photonics provides a robust and flexible platform for controlling light, enabling functionalities such as backscattering-immune edge transport and slow-light propagation. In this work, we design and characterize photonic…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
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…
Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($\varphi$), permeability $k$, and tortuosity ($T$). The…
An universal invariant for site and bond percolation thresholds (p_{cs} and p_{cb} respectively) is proposed. The invariant writes {p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=\delta/d where a_s, a_b and \delta are positive constants,and d the space…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…