Related papers: Nucleation pathways on complex networks
The nucleation of crystals from the liquid melt is often characterized by a competition between different crystalline structures or polymorphs, and can result in nuclei with heterogeneous compositions. These mixed-phase nuclei can display…
We investigate heterogeneous and homogeneous nucleation in nearest-neighbor and long-range Ising models for various quench depths. We find that the system has a true crossover from heterogeneous to homogeneous nucleation for increasing…
A major issue in biology is the understanding of the interactions between proteins. These interactions can be described by a network, where the proteins are modeled by nodes and the interactions by edges. The origin of these protein…
Crystallization of supersaturated liquids usually starts by heterogeneous nucleation. Mounting evidence shows that even homogeneous nucleation in simple liquids takes place in two steps; first a dense amorphous precursor forms, and the…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
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…
We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process…
Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore,…
Nucleation is generally viewed as a structural fluctuation that passes a critical size to eventually become a stable emerging new phase. However, this concept leaves out many details, such as changes in cluster composition and competing…
Nucleation and growth is the dominant relaxation mechanism driving first order phase transitions. In two-dimensional at systems nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
NaCl crystal nucleation from metastable solutions has long been considered to occur according to a single-step mechanism. Recent experimental observations suggest that NaCl crystals emerge from disordered intermediates which is seemingly at…
Homogeneous nucleation of a new phase near an Ising-like critical point of another phase transition is studied. A scaling analysis shows that the free energy barrier to nucleation contains a singular term with the same scaling as the order…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Complex contagion adoption dynamics are characterised by a node being more likely to adopt after multiple network neighbours have adopted. We show how to construct multi-type branching processes to approximate complex contagion adoption…
In this review we summarize our recent efforts in trying to understand the role of heterogeneity in cancer progression by using neural networks to characterise different aspects of the mapping from a cancer cells genotype and environment to…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
We investigate the effect of phase randomness in Ising-type quantum networks. These networks model a large class of physical systems. They describe micro- and nanostructures or arrays of optical elements such as beam splitters…