Phase diagrams of the Ziff–Gulari–Barshad model on random networks

Abstract

In this study, we revisited the Ziff–Gulari–Barshad (ZGB) model in order to study the behavior of its phase diagram when two well‐known random networks play the role of the catalytic surfaces: the random geometric graph and the Erdös–Rényi network. The connectivity and, therefore, the average number of neighbors of the nodes of these networks can vary according to their control parameters, the neighborhood radius α, and the linking probability p, respectively. In addition, the catalytic reactions of the ZGB model are governed by the parameter y, the adsorption rate of carbon monoxide molecules on the catalytic surface. So, to study the phase diagrams of the model on both random networks, we carried out extensive steady‐state Monte Carlo simulations in the space parameters (y, α) and (y, p) and showed that the continuous phase transition is greatly affected by the topological features of the networks while the discontinuous one remains present in the diagram throughout the interval of study.

Topological transition in a coupled dynamic in random networks

“…In this way, the average degree K of the network varies from K = 0, for r = 0, to K = M − 1, when r ≥ z √ 2/2 (half the diagonal of the square). This random geometric graph is the originally random graph introduced to model wireless communication networks [40] and it has been recently used with different applications [8,[41][42][43][44].…”

“…As presented above, the connectivity in the RGG network is controlled by its radius r [44]. In this work, in order to look into the phase transition of the model, we set the region of interest as the range 0.5 < r < 3.0.…”

Theoretical study of the competition between folding and contact interactions on the properties of polymers using self-avoid random walk algorithm

“…Different theoretical methods have been used to study the properties of polymer [11][12][13][14][15][16]. Many of these methods fall on the area of Statistical Mechanics, when probabilistic methods are evaluated and the results are the average values [17,18]. In this approach, one simple algorithm that has been extensively used to generate the trajectories representing the polymers is the Self-Avoid Random Walk, or SAW [19,20].…”

Insights into the effect of growth on the Ziff–Gulari–Barshad model and the film properties

“…Because of the importance of this heterogeneous catalytic process along with the simplicity of the ZGB model many works have been published which add mechanisms or alter existing ones in order to study the dynamical characteristics of the system, i.e. the phase transition; alternative lattices [2,3], 'hot' dimer adsorption [4][5][6][7], repulsive interactions [8][9][10], diffusion [11][12][13][14], long range reactivity [15], Elley-Rideal type mechanism [16], periodic CO pressure [17][18][19][20], impurities [21][22][23][24][25][26][27], first principle assisted kinetic Monte Carlo (KMC) calculations [28,29] experiments [30][31][32] and more recent theoretical works [33][34][35][36][37].…”