Biomedical Applications of Metal 3D Printing.

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.

Distribution of blackouts in the power grid and the Motter and Lai model.

Carreras, Dobson, and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them with computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system.

Network overload due to massive attacks.

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.

Cascading failures in networks with proximate dependent nodes.

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 nontrivial 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.