scholarly journals Explosive Percolation in Erdős–Rényi-Like Random Graph Processes

2012 ◽  
Vol 22 (1) ◽  
pp. 133-145 ◽  
Author(s):  
KONSTANTINOS PANAGIOTOU ◽  
RETO SPÖHEL ◽  
ANGELIKA STEGER ◽  
HENNING THOMAS
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Random Graph ◽  
Continuous Phase ◽  
Selection Rules ◽  
Continuous Phase Transition ◽  
Empty Graph ◽  
Numerical Evidence ◽  
Discontinuous Phase ◽  
Discontinuous Phase Transitions

The study of the phase transition of random graph processes, and recently in particular Achlioptas processes, has attracted much attention. Achlioptas, D'Souza and Spencer (Science, 2009) gave strong numerical evidence that a variety of edge-selection rules in Achlioptas processes exhibit a discontinuous phase transition. However, Riordan and Warnke (Science, 2011) recently showed that all these processes have a continuous phase transition.In this work we prove discontinuous phase transitions for three random graph processes: all three start with the empty graph on n vertices and, depending on the process, we connect in every step (i) one vertex chosen randomly from all vertices and one chosen randomly from a restricted set of vertices, (ii) two components chosen randomly from the set of all components, or (iii) a randomly chosen vertex and a randomly chosen component.

scholarly journals Is Independence Necessary for a Discontinuous Phase Transition within the q-Voter Model?

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 521 ◽  
Author(s):  
Angelika Abramiuk ◽  
Jakub Pawłowski ◽  
Katarzyna Sznajd-Weron
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Continuous Phase ◽  
Voter Model ◽  
Social Response ◽  
Generalized Model ◽  
Independent Variables ◽  
The Social ◽  
Discontinuous Phase ◽  
Independent Behavior

We ask a question about the possibility of a discontinuous phase transition and the related social hysteresis within the q-voter model with anticonformity. Previously, it was claimed that within the q-voter model the social hysteresis can emerge only because of an independent behavior, and for the model with anticonformity only continuous phase transitions are possible. However, this claim was derived from the model, in which the size of the influence group needed for the conformity was the same as the size of the group needed for the anticonformity. Here, we abandon this assumption on the equality of two types of social response and introduce the generalized model, in which the size of the influence group needed for the conformity q c and the size of the influence group needed for the anticonformity q a are independent variables and in general q c ≠ q a . We investigate the model on the complete graph, similarly as it was done for the original q-voter model with anticonformity, and we show that such a generalized model displays both types of phase transitions depending on parameters q c and q a .

scholarly journals Continuous phase transitions on Galton–Watson trees

2021 ◽  
pp. 1-31
Author(s):  
Tobias Johnson
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Discrete Systems ◽  
Continuous Phase ◽  
Recursive Structure ◽  
Continuous Phase Transition ◽  
First Order ◽  
First Order Phase Transition ◽  
The Mean ◽  
First Order Phase

Abstract Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galton–Watson trees. For example, let $\mathcal{T}_1$ be the event that a Galton–Watson tree is infinite and let $\mathcal{T}_2$ be the event that it contains an infinite binary tree starting from its root. These events satisfy similar recursive properties: $\mathcal{T}_1$ holds if and only if $\mathcal{T}_1$ holds for at least one of the trees initiated by children of the root, and $\mathcal{T}_2$ holds if and only if $\mathcal{T}_2$ holds for at least two of these trees. The probability of $\mathcal{T}_1$ has a continuous phase transition, increasing from 0 when the mean of the child distribution increases above 1. On the other hand, the probability of $\mathcal{T}_2$ has a first-order phase transition, jumping discontinuously to a non-zero value at criticality. Given the recursive property satisfied by the event, we describe the critical child distributions where a continuous phase transition takes place. In many cases, we also characterise the event undergoing the phase transition.

Characterizing multiple continuous phase transitions at an alloying anode with voltammetric measurements and first-principles calculations

2019 ◽  
Vol 7 (40) ◽  
pp. 23121-23129 ◽  
Author(s):  
Yong-Seok Choi ◽  
Jae-Chul Lee
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
First Principles ◽  
Continuous Phase ◽  
First Principles Calculations ◽  
Continuous Phase Transition ◽  
Voltammetric Measurement ◽  
Voltammetric Measurements

In this study, a combination of first-principles calculations and voltammetric measurement is used to identify multiple and continuous phase transition behaviors at the Sb anode during the Na–Sb battery cycles.

scholarly journals Propagation of pop ups in kirigami shells

2019 ◽  
Vol 116 (17) ◽  
pp. 8200-8205 ◽  
Author(s):  
Ahmad Rafsanjani ◽  
Lishuai Jin ◽  
Bolei Deng ◽  
Katia Bertoldi
Keyword(s):  
Continuous Phase ◽  
Large Strains ◽  
Linear Actuator ◽  
Continuous Phase Transition ◽  
Responsive Surfaces ◽  
Out Of Plane ◽  
Discontinuous Phase ◽  
Smart Skin ◽  
Discontinuous Phase Transitions ◽  
Shape Changes

Kirigami-inspired metamaterials are attracting increasing interest because of their ability to achieve extremely large strains and shape changes via out-of-plane buckling. While in flat kirigami sheets, the ligaments buckle simultaneously as Euler columns, leading to a continuous phase transition; here, we demonstrate that kirigami shells can also support discontinuous phase transitions. Specifically, we show via a combination of experiments, numerical simulations, and theoretical analysis that, in cylindrical kirigami shells, the snapping-induced curvature inversion of the initially bent ligaments results in a pop-up process that first localizes near an imperfection and then, as the deformation is increased, progressively spreads through the structure. Notably, we find that the width of the transition zone as well as the stress at which propagation of the instability is triggered can be controlled by carefully selecting the geometry of the cuts and the curvature of the shell. Our study significantly expands the ability of existing kirigami metamaterials and opens avenues for the design of the next generation of responsive surfaces as demonstrated by the design of a smart skin that significantly enhances the crawling efficiency of a simple linear actuator.

scholarly journals Understanding the Influence of Measurement Uncertainty on the Atmospheric Transition in Rainfall and Column Water Vapor

2015 ◽  
Vol 72 (5) ◽  
pp. 2041-2054 ◽  
Author(s):  
James B. Gilmore
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Water Vapor ◽  
Measurement Uncertainty ◽  
Rain Rate ◽  
Tropical Rainfall Measuring Mission ◽  
Continuous Phase ◽  
Large Variability ◽  
Continuous Phase Transition ◽  
Rain Rates

Abstract Measurement uncertainty plays a key role in understanding physical relationships. This is particularly the case near phase transitions where order parameters undergo fast changes and display large variability. Here the proposed atmospheric continuous phase transition is examined by analyzing uncertainty in rain-rate and column water vapor measurements from the Tropical Rainfall Measuring Mission and through an idealized error analysis. It is shown through both of these approaches that microwave rain-rate retrievals can mimic a continuous phase transition. This occurs because microwave retrievals of instantaneous rain rates have a suppressed range. This work also suggests that column water vapor noise may provide part of the plateau seen in the observational relationship. Using updated measurements, this work indicates that the atmosphere is unlikely to undergo a continuous phase transition in rain rate but, instead, contains much larger variability in rain rates at extreme column water vapor values than previously thought. This implies that the atmosphere transitions from a low-variance nonraining state to a high-variance raining state at extreme column water vapor values.

scholarly journals Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

2020 ◽  
Vol 125 (26) ◽  
Author(s):  
Norifumi Matsumoto ◽  
Kohei Kawabata ◽  
Yuto Ashida ◽  
Shunsuke Furukawa ◽  
Masahito Ueda
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Many Body ◽  
Continuous Phase Transition ◽  
Many Body Systems ◽  
Gap Closing

Higher Order Criteria on the Continuous Phase Transition

1989 ◽  
Vol 58 (3) ◽  
pp. 898-904
Author(s):  
Ruibao Tao ◽  
Xiao Hu ◽  
Masuo Suzuki
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Higher Order ◽  
Continuous Phase Transition

Percolation phase transition of static and growing networks under a weighted function

2016 ◽  
Vol 27 (07) ◽  
pp. 1650082 ◽  
Author(s):  
Xiao Jia ◽  
Jin-Song Hong ◽  
Ya-Chun Gao ◽  
Hong-Chun Yang ◽  
Chun Yang ◽  
...  
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Weighted Function ◽  
Percolation Process ◽  
Practical Applications ◽  
Network Intervention ◽  
Growing Networks ◽  
Discontinuous Phase ◽  
And Control ◽  
Growing Network

We investigate the percolation phase transitions in both the static and growing networks where the nodes are sampled according to a weighted function with a tunable parameter [Formula: see text]. For the static network, i.e. the number of nodes is constant during the percolation process, the percolation phase transition can evolve from continuous to discontinuous as the value of [Formula: see text] is tuned. Based on the properties of the weighted function, three typical values of [Formula: see text] are analyzed. The model becomes the classical Erdös–Rényi (ER) network model at [Formula: see text]. When [Formula: see text], it is shown that the percolation process generates a weakly discontinuous phase transition where the order parameter exhibits an extremely abrupt transition with a significant jump in large but finite system. For [Formula: see text], the cluster size distribution at the lower pseudo-transition point does not obey the power-law behavior, indicating a strongly discontinuous phase transition. In the case of growing network, in which the collection of nodes is increasing, a smoother continuous phase transition emerges at [Formula: see text], in contrast to the weakly discontinuous phase transition of the static network. At [Formula: see text], on the other hand, probability modulation effect shows that the nature of strongly discontinuous phase transition remains the same with the static network despite the node arrival even in the thermodynamic limit. These percolation properties of the growing networks could provide useful reference for network intervention and control in practical applications in consideration of the increasing size of most actual networks.

scholarly journals Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Jesus M. Encinas ◽  
Pedro E. Harunari ◽  
M. M. de Oliveira ◽  
Carlos E. Fiore
Keyword(s):  
Phase Transitions ◽  
Majority Vote ◽  
Vote Model ◽  
Discontinuous Phase ◽  
Discontinuous Phase Transitions

ATMOSPHERIC CONVECTION AS A CONTINUOUS PHASE TRANSITION: FURTHER EVIDENCE

2009 ◽  
Vol 23 (28n29) ◽  
pp. 5453-5465 ◽  
Author(s):  
OLE PETERS ◽  
J. DAVID NEELIN
Keyword(s):  
Phase Transition ◽  
Hurricane Katrina ◽  
Rain Rate ◽  
Extreme Event ◽  
Atmospheric Precipitation ◽  
Continuous Phase ◽  
Critical Parameters ◽  
Continuous Phase Transition ◽  
Scale Free ◽  
Tuning Parameters

We present further methods to investigate in how far atmospheric precipitation can be described as a continuous phase transition. Previous work has shown a scale-free range in the rainfall event size distribution and a suggestive power-law pickup in the rain rate above a critical level of instability. Here we examine an additional technique for estimating critical parameters, we investigate the rain rate pickup for an example of an extreme event, namely satellite observations of Hurricane Katrina, and develop an analysis of fluctuations in the rain rate to estimate uncertainties in the tuning parameters relevant for the transition.

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