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Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem. This anomalous transition occurs in networks of three or more layers without unconnected nodes, P (0) = 0 . Above a critical value of a control parameter, the removal of a tiny fraction Δ of nodes or edges triggers a failure cascade which ends either with the total collapse of the network, or a return to stability with the system essentially intact. The discontinuity is not accompanied by any singularity of the giant component, in contrast to the discontinuous hybrid transition which usually appears in such problems. The control parameter is the fraction of nodes in each layer with a single connection, Π = P (1) . We obtain asymptotic expressions for the collapse time and relaxation time, above and below the critical point Π c , respectively. In the limit Δ → 0 the total collapse for Π > Π c takes a time T ∝ 1 / (Π - Π c) , while there is an exponential relaxation below Π c with a relaxation time τ ∝ 1 / [ Π c - Π ] . [ABSTRACT FROM AUTHOR]

We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random damage. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge. [ABSTRACT FROM AUTHOR]

We introduce the heterogeneous k-core, which generalizes the k-core, and contrast it with bootstrap percolation. Vertices have a threshold ri that may be different at each vertex. If a vertex has fewer than ri neighbors it is pruned from the network. The heterogeneous k-core is the subgraph remaining after no further vertices can be pruned. If the thresholds ri are 1 with probability ƒ, or k ⩾ 3 with probability 1 - ƒ, the process can be thought of as a pruning process counterpart to ordinary bootstrap percolation, which is an activation process. We show that there are two types of transitions in this heterogeneous k-core process: the giant heterogeneous k-core may appear with a continuous transition and there may be a second discontinuous hybrid transition. We compare critical phenomena, critical clusters, and avalanches at the heterogeneous k-core and bootstrap percolation transitions. We also show that the network structure has a crucial effect on these processes, with the giant heterogeneous k-core appearing immediately at a finite value for any ƒ > 0 when the degree distribution tends to a power law P(q) ∼ q-γ with γ < 3. [ABSTRACT FROM AUTHOR]

Compression, filtering, and cryptography, as well as the sampling of complex systems, can be seen as processing information. A large initial configuration or input space is nontrivially mapped to a smaller set of output or final states. We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable example of such information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring, we obtained an exact solution of the problem and numerically described more difficult filter setups. For each of the filter patterns and networks, we found three key numbers that essentially describe the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures are essentially determined by two factors: whether the graphs structure is deterministic or random and the vertex degree. We find that filtering in random graphs produces much richer statistics than in deterministic graphs, reflecting the greater complexity of such graphs. Increasing the graph's degree reduces this statistical richness, while being at its maximum at the smallest degree not equal to two. A filter pattern with a strong dependence on the neighbourhood of a node is much more sensitive to these effects. [ABSTRACT FROM AUTHOR]

Complex systems consisting of interdependent subsystems may be represented by multilayer networks with interdependency links between layers. The giant mutually connected component (GMCC) of such an interdependent (or multiplex) network collapses with a discontinuous hybrid transition under random damage to the network. If the nodes to be damaged are selected in a targeted way, the collapse of the GMCC may occur significantly sooner. Understanding the limits of the resilience of such systems to targeted attacks is therefore an essential problem. Finding the minimal damage set which destroys the largest mutually connected component of a given interdependent network is a computationally prohibitive simultaneous optimization problem. We introduce a simple heuristic strategy--effective multiplex degree--for targeted attack on interdependent networks that leverages the indirect damage inherent in multiplex networks to achieve a damage set smaller than that found by any existing noncomputationally intensive algorithm. We show that the intuition from single-layer networks that decycling (damage of the 2-core) is the most effective way to destroy the giant component does not carry over to interdependent networks and in fact such approaches are worse than simply removing the highest degree nodes. [ABSTRACT FROM AUTHOR]

Metal additive manufacturing techniques typically operate using powders with limited particle size ranges, but atomisation processes produce significant amounts of particles outside these ranges, resulting in an accumulation of out-of-size specification metal powders without a clear use case. Field-assisted sintering technology (FAST) can provide an alternative, solid-state processing route to consolidate these powders into billets for subsequent processing, or directly into near-net shape components. In this study, surplus powders of A20X, an aerospace approved aluminium alloy developed by Aluminium Materials Technologies (ECKART GmbH), were processed using FAST and subsequently hot rolled to produce sheet material. Tensile properties were similar to hot rolled conventional cast material and comparable to additively manufactured product. This indicates that FAST is an effective option for converting surplus metal powders into useful products, while improving sustainability in the additive supply chain. [ABSTRACT FROM AUTHOR]

Predictions of residual stresses in inertia friction welded Ni-base superalloys have been carried out using a commercial finite element code (DEFORM) combined with an energy balance approach and a 2D axisymmetric formulation. A coupled thermal and mechanical finite element model has been created. During inertia welding trials of RR1000, a high Υ ' Ni-base superalloy, the rotational velocity and upset history curves were recorded. From these data the heat flux (the rate of energy input) through the weld interface was inferred and together with the upsetting rate input into the model as evolving boundary conditions. The coupled thermal and mechanical analysis leads to the prediction of the thermal history and the residual stresses generated during cooling. The validation of the model has been undertaken by comparing the predicted residual stresses with those measured using neutron diffraction. The comparison between predicted and measured stresses is in good agreement. [ABSTRACT FROM AUTHOR]