Phase transition of the 2-Choices dynamics on core–periphery networks

The 2-Choices dynamics is a process that models voting behavior on networks and works as follows: Each agent initially holds either opinion blue or red; then, in each round, each agent looks at two random neighbors and, if the two have the same opinion, the agent adopts it. We study its behavior on a class of networks with core–periphery structure. Assume that a densely-connected subset of agents, the core, holds a different opinion from the rest of the network, the periphery. We prove that, depending on the strength of the cut between core and periphery, a phase-transition phenomenon occurs: Either the core’s opinion rapidly spreads across the network, or a metastability phase takes place in which both opinions coexist for superpolynomial time. The interest of our result, which we also validate with extensive experiments on real networks, is twofold. First, it sheds light on the influence of the core on the rest of the network as a function of its connectivity toward the latter. Second, it is one of the first analytical results which shows a heterogeneous behavior of a simple dynamics as a function of structural parameters of the network.

Exploration of Structural Transition Phenomenon in Flexible Metal-Organic Framework Formed on Polymer Substrate

Control of structural transition in flexible metal-organic frameworks (MOFs) on a substrate is crucial for controlling their properties for the development of MOF-based applications. In this study, we investigate the...

Transitive Methods

Chapter 2, devoted to deterministic transitive methods, introduces the notion of a transition phenomenon by using the example of the indicator function of a set, which is described by means of its geometrical covariogram. This notion is then extended to any numerical function f of the space. The next step consists in studying in detail the operation of ‘grading’ in the isotropic case, where the initial pointwise regionalised variable is replaced by its regularised average along a line, as would occur during drilling. Simple rules for passing from the pointwise covariogram to the graded one are given. When the regionalised variable is recognised by a regular grid whose origin has a random setting, the integral of function f becomes a random variable. Its estimation variance is expressed in terms of the covariogram, and the rules about regularisation allow the numerical computation of this variance. The case of set indicators is treated in detail.

Contrastive Studies between Laser Repairing and Plasma Arc Repairing on Single-Crystal Ni-Based Superalloy

Laser repairing and plasma arc repairing experiments on the single-crystal Ni-based superalloy DD407(Ni-7.82Cr-5.34Co-2.25Mo-4.88W-6.02Al-1.94Ti-3.49Ta in wt.%) were carried out in this paper, and the differences in microstructures and mechanical properties varying with depth between the two repairing methods were studied. Comparing the two repairing processes, both the fusion zone can maintain single-crystal epitaxial growth with no significant cracks and have similar fine γ′ precipitates. Nevertheless, the columnar-to-equiaxed transition phenomenon occurred on the top of the fusion zone during the laser re-melting process but was not very obvious on the top surface of the fusion zone during the plasma arc re-melting process. In addition, both the DD407 superalloy conducted with the two repairing processes had a large microhardness and a great Young’s modulus in the fusion zone.