Related papers: Universal discontinuous percolation transition in …
We propose an approach to calculate the critical percolation threshold for finite-sized Erdos-Renyi digraphs using minimal Hamiltonian cycles. We obtain an analytically exact result, valid non-asymptotically for all graph sizes, which…
Domain growth during the kinetics of phase separation is studied following vapor-liquid transition in a single component Lennard-Jones fluid. Results are analyzed after appropriately mapping the continuum snapshots obtained from extensive…
Using three-dimensional representation of confluent cell layers, we map the amorphous solid to fluid phase transition in active cell layers onto the two-dimensional (2D) site percolation universality class. Importantly, we unify two…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The…
We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites…
Earth's modern climate is characterized by wet, rainy deep tropics, however paleoclimate and planetary science have revealed a wide range of hydrological cycle regimes connected to different external parameters. Here we investigate how…
Changes that occur on our planet can be tracked back to one of two energy sources: the sun and the Earth's internal energy. The motion of tectonic plates, volcanism, mountain building and the reshaping of our planet's surface over geologic…
We study the dynamics of corotational wave maps from $\mathbb R^{1+2} \rightarrow \mathbb S^2$ at threshold energy. It is known that topologically trivial wave maps with energy $< 8\pi$ are global and scatter to a constant map. In this…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
Although realizing wetting transitions of droplets spontaneously on solid rough surfaces is quite challenging, it is becoming a key research topic in many practical applications which require highly efficient removal of liquid. We report…
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
Because the solar luminosity increases over geological timescales, Earth climate is expected to warm, increasing water evaporation which, in turn, enhances the atmospheric greenhouse effect. Above a certain critical insolation, this…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…
The recent proliferation of correlated percolation models---models where the addition of edges/vertices is no longer independent of other edges/vertices---has been motivated by the quest to find discontinuous percolation transitions. The…
The concept of midpoint percolation has recently been applied to characterize the double percolation transitions in negatively curved structures. Regular $d$-dimensional hypercubic lattices are in the present work investigated using the…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of…
Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant…
We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum…