Microtransition Cascades to Percolation

Chen, Wei; Schröder, Malte; D’Souza, Raissa M.; Sornette, Didier; Nagler, Jan

doi:10.1103/physrevlett.112.155701

Cited by 75 publications

(82 citation statements)

References 37 publications

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“…Also shown recently is that microscopic patterns in the early evolution of percolation processes can be used to predict the location of the critical point 73 . In particular, the generalized BFW process exhibits peaks in relative variance at well-defined values of t i (with i an integer), which survive in the thermodynamic limit (see Fig.…”

Section: Disordered Mediamentioning

confidence: 99%

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Anomalous critical and supercritical phenomena in explosive percolation

2015

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The emergence of large-scale connectivity on an underlying network or lattice, the so-called percolation transition, has a profound impact on the system's macroscopic behaviours. There is thus great interest in controlling the location of the percolation transition to either enhance or delay its onset and, more generally, in understanding the consequences of such control interventions. Here we review explosive percolation, the sudden emergence of large-scale connectivity that results from repeated, small interventions designed to delay the percolation transition. These transitions exhibit drastic, unanticipated and exciting consequences that make explosive percolation an emerging paradigm for modelling real-world systems ranging from social networks to nanotubes.T he percolation transition, named for the prototypical mathematical problem of pouring liquid through a porous material, describes the onset of large-scale connectivity on an underlying network or lattice. At times, ensuring large-scale connectivity is essential: a transportation network (such as the world-wide airline network) or a communication system (such the Internet) is useful only if a large fraction of the nodes are connected. Yet, in other contexts, large-scale connectivity is a liability: under certain conditions, a virus spreading on a well-connected social or computer network can reach enough nodes to cause an epidemic. Thus, percolation theory is a theoretical underpinning across a range of fields 1,2 and the desire to enhance or delay the onset of percolation has been of interest for many years. The consequences of delaying the transition have only recently been established and here we review explosive percolation (EP), the phenomenon that usually results from repeated, small interventions designed to delay the percolation transition. The onset can indeed be significantly delayed, but once the percolation transition is inevitably reached, large-scale connectivity emerges suddenly.The traditional approach for constructing a random graph, the Erdős-Rényi model, considers a collection of N isolated nodes, with each possible edge between two distinct nodes added to the graph with probability p (refs 3-5). This is a static formulation with no dependence on the history of how edges have been added to the graph. A mathematically equivalent kinetic formulation is initialized with N originally isolated nodes with a randomly sampled edge added at each discrete time step 6 . Letting T denote the number of steps, the process is parameterized by the relative number of introduced edges t = T /N , and typically analysed in the thermodynamic limit of infinite size N . Below some critical t = t c the resulting graph is disjoint, consisting of small isolated clusters (or components) of connected nodes. (See Fig. 1c for an illustration of distinct components.) Let C denote the largest component and |C| its size. For the Erdős-Rényi model, the order parameter |C| undergoes a second-order transition at t c = 1/2 where, below t c , |C| is logarithmic in N and, a...

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Section: Disordered Mediamentioning

confidence: 99%

“…The positions of the peaks t i obey a discrete scale invariance 74 (meaning that scale invariance holds only for a discrete set of magnification factors). We can predict the critical point t i → t c from the discrete scaling relation 73 . Non-self-averaging behaviours can thus provide a powerful predictive tool.…”

Section: Disordered Mediamentioning

confidence: 99%

Anomalous critical and supercritical phenomena in explosive percolation

2015

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“…Large anomalous Hall (AHE) and Nernst effects that used to be observed from ferromagnets only 66,67 have been recently observed from chiral non-collinear antiferromagnets 68 such as Mn3Sn 69 , Mn3Ir 61 , and Mn3Ge 71 due to non-vanishing Berry phase. These exotic materials exhibit small coercivity allowing the large magneto-transport coefficients to be used as readouts in chiral antiferromagnets-based devices.…”

Section: Chiral Magnetic Skyrmions 2d Chiral Magnetic Objects In Conmentioning

confidence: 99%

Spintronics on chiral objects

Yang

2020

Applied Physics Letters

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Chirality, handedness, is one of the most fundamental intriguing asymmetries in nature. By definition, chiral objects cannot be superimposed onto each other after mirror reflection operation. Numerous examples of chiral structures can be found in nature, for example, chiral molecules and chiral magnetic nanostructures. Moving electrons are associated with handedness by their own spins due to spin-orbit interaction thus exhibiting various emergent phenomena as they interact with chiral materials, which otherwise would not be observed in achiral systems. This new paradigm allows the potential development of new forms of devices or methods by utilizing reciprocal interaction of chiral objects with moving electron spins. This review updates the remarkable progresses in Spintronics on Chiral Objects that have been made over the past few years providing provides an outlook for new opportunities and potential applications with new insights.

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“…2). Indeed, according to the definition (6), the form (20) implies the universal decay c k ∼ [t(ln t) 2 ] −1 for all small and finite k, in contradiction with the three distinct types of asymptotic behavior summarized in (17).…”

Section: Maximal Choicementioning

confidence: 93%

“…In summary, equations (12), (13), and (16) show that there are three distinct scaling laws for small clusters of monomers, dimers, and clusters of mass 3 ≤ k t. As we show below, the scaling function underlying the cluster-size density captures c k with k ≥ 3. We stress that whether the logarithmic terms in (17) are ignored or retained, the difference between maximal choice and ordinary aggregation where c k ∼ t −2 becomes more and more pronounced as time increases.…”

Section: Maximal Choicementioning

confidence: 99%

Kinetics of aggregation with choice

Ben‐Naim

Krapivsky

2016

Phys. Rev. E

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We generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice, a target cluster and two candidate clusters are randomly selected, and the target cluster merges with the larger of the two candidate clusters. We study the long-time asymptotic behavior, and find that as in ordinary aggregation, the size density adheres to the standard scaling form. However, aggregation with choice exhibits a number of novel features. First, the density of the smallest clusters exhibits anomalous scaling. Second, both the small-size and the large-size tails of the density are overpopulated, at the expense of the density of moderate-size clusters. We also study the complementary case where the smaller candidate cluster participates in the aggregation process, and find abundance of moderate clusters at the expense of small and large clusters. Additionally, we investigate aggregation processes with choice among multiple candidate clusters, and a symmetric implementation where the choice is between two pairs of clusters.

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Microtransition Cascades to Percolation

Cited by 75 publications

References 37 publications

Anomalous critical and supercritical phenomena in explosive percolation

Anomalous critical and supercritical phenomena in explosive percolation

Spintronics on chiral objects

Kinetics of aggregation with choice

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