Related papers: Scaling in Local Optimal Paths Cracks
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
While cracking is a complex dynamics that involves material intrinsic properties like grain shape and size distribution, elastic properties of grain and cementing materials, and extrinsic properties of loading, in this work, the focus has…
A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…
Recent empirical studies have reported that spatiotemporal congestion clusters in urban traffic exhibit scale-free statistics, with cluster size following a power-law distribution. In this study, we address whether macroscopic continuum…
Routing, modulation and spectrum allocation in elastic optical networks is a problem aiming at increasing the capacity of the network. Many algorithms such as shortest path algorithm can be used as the routing section of this problem. The…
We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
While we fundamentally understand the dynamics of 'simple' cracks propagating in brittle solids within perfect (homogeneous) materials, we do not understand how paths of moving cracks are determined. We experimentally study strongly…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…
We consider the problem of distributed optimal power flow (OPF) for multi-area electric power systems. A novel distributed algorithm is proposed, referred to as the rotated coordinate descent critical region exploration (RCDCRE). It allows…
Prompt and effective corrective actions in response to unexpected contingencies are crucial for improving power system resilience and preventing cascading blackouts. The optimal load shedding (OLS) accounting for network limits has the…
For linear-quadratic optimal control problems (OCPs) governed by elliptic and parabolic partial differential equations (PDEs), we investigate the impact of perturbations on optimal solutions. Local perturbations may occur, e.g., due to…
Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
This work proposes a novel method for scaling multi-timestep security-constrained optimal power flow in large power grids. The challenge arises from dealing with millions of variables and constraints, including binary variables and…
One of the central models in distributed computing is Linial's LOCAL model [SIAM J. Comp. 1992]. Over time, researchers have studied distributed graph problems in the LOCAL model under slightly different assumptions, such as whether nodes…
Many problems arise in computational biology can be reduced to the minimization of energy function, that determines on the geometry of considered molecule. The solution of this problem allows in particular to solve folding and docking…
Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected…