We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an initial attack. We find a non-trivial relation between the nature of the transition through which the networks disintegrate and the parameters of the system, which are the degree of the nodes and the maximum distance between interdependent nodes. We explain this relation by solving the problem analytically for the relevant set of cases.Previous studies of the robustness of interdependent networks have focused on networks in which there is no constraint on the distance between the interdependent nodes [1][2][3][4][5][6][7][8][9]. However, many dependency links in the real world connect nearby nodes. For example, the international network of seaports and the network of national highways form a complex system. As seen recently from the effects of Hurricane Sandy in New York City, if a seaport is damaged, the city that depends on it will become isolated from the highway network due to the lack of fuel. Similarly, a city without roads cannot supply a seaport properly. However, a city will depend on a nearby seaport, not on one across the world. Li et. al [10] investigated distance-limited interdependent lattice networks by computer simulations and found that allowing only local interdependency links changed the resilience properties of the system. Here, we study the analytically tractable random networks. We study the mutual percolation of two interdependent random regular (RR) graphs. We build two identical networks, A and B, each of whose nodes are labeled 1...N . Each node is randomly connected by edges to exactly k other nodes, in such a way that the two networks have identical topologies. We then create one-to-one bidirectional dependency links, requiring that the shortest path between the interdependent nodes does not exceed an integer constant ℓ. Formally, we establish two isomorphisms between networks A and B, a topological isomorphism and a dependency isomorphism. The topological isomorphism is defined for each node A i as T (A i ) = B i and T (B i ) = A i . If Following the mutual percolation model described in Buldyrev et al.[1], we destroy a fraction (1 − p) of randomly selected nodes in A. Any nodes that, as a result, lost their connectivity links to the largest cluster (as defined in classical, single-network percolation theory [11,12]) are also destroyed. In the next stage, nodes in B that have their interdependent nodes in the other network destroyed are also destroyed. Consequently, the nodes that are isolated from the largest cluster in B as a result of the destruction of nodes in B are also destroyed. The iteration of this process, which alternates between the two networks, leads to a cascade of failures. The cascade ends when no more nodes fail in either network. The pair of remaining largest interdependent clusters in both networks is called a largest mutual componen...

Additive manufacturing's attributes include print customization, low per-unit cost for small- to mid-batch production, seamless interfacing with mainstream medical 3D imaging techniques, and feasibility to create free-form objects in materials that are biocompatible and biodegradable. Consequently, additive manufacturing is apposite for a wide range of biomedical applications including custom biocompatible implants that mimic the mechanical response of bone, biodegradable scaffolds with engineered degradation rate, medical surgical tools, and biomedical instrumentation. This review surveys the materials, 3D printing methods and technologies, and biomedical applications of metal 3D printing, providing a historical perspective while focusing on the state of the art. It then identifies a number of exciting directions of future growth: ( a) the improvement of mainstream additive manufacturing methods and associated feedstock; ( b) the exploration of mature, less utilized metal 3D printing techniques; ( c) the optimization of additively manufactured load-bearing structures via artificial intelligence; and ( d) the creation of monolithic, multimaterial, finely featured, multifunctional implants.

We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade p_{f} as a function of the strength of the initial attack, measured by the fraction of nodes p that survive the initial attack for different values of tolerance α in random regular and Erdös-Renyi graphs. We find the existence of a first-order phase-transition line p_{t}(α) on a p-α plane, such that if pp_{t}, p_{f} is large and the giant component of the network is still present. Exactly at p_{t}, the function p_{f}(p) undergoes a first-order discontinuity. We find that the line p_{t}(α) ends at a critical point (p_{c},α_{c}), in which the cascading failures are replaced by a second-order percolation transition. We find analytically the average betweenness of nodes with different degrees before and after the initial attack, we investigate their roles in the cascading failures, and we find a lower bound for p_{t}(α). We also study the difference between localized and random attacks.

We present the field-line modeling, design and construction of a prototype circular-coil tokamak-torsatron hybrid called Proto-CIRCUS. The device has a major radius R = 16 cm and minor radius a < 5 cm. The six "toroidal field" coils are planar as in a tokamak, but they are tilted. This, combined with induced or driven plasma current, is expected to generate rotational transform, as seen in field-line tracing and equilibrium calculations. The device is expected to operate at lower plasma current than a tokamak of comparable size and magnetic field, which might have interesting implications for disruptions and steady-state operation. Additionally, the toroidal magnetic ripple is less pronounced than in an equivalent tokamak in which the coils are not tilted. The tilted coils are interlocked, resulting in a relatively low aspect ratio, and can be moved, both radially and in tilt angle, between discharges. This capability will be exploited for detailed comparisons between calculations and field-line mapping measurements. Such comparisons will reveal whether this relatively simple concept can generate the expected rotational transform.