Related papers: Evolution of Semilocal String Networks: II. Veloci…

For many random graph models, the analysis of a related birth process suggests local sampling algorithms for the size of, e.g., the giant connected component, the $k$-core, the size and probability of an epidemic outbreak, etc. In this…

We study the temporal evolution of the structure of the world's largest subway networks in an exploratory manner. We show that, remarkably, all these networks converge to {a shape which shares similar generic features} despite their…

For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…

Researchers have devoted themselves to exploring static features of social networks and further discovered many representative characteristics, such as power law in the degree distribution and assortative value used to differentiate social…

We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…

Models of symmetry breaking in the early universe can produce networks of cosmic strings threading 't Hooft-Polyakov monopoles. In certain cases there is a larger global symmetry group and the monopoles split into so-called semipoles. These…

Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…

We study the dynamics of strings by means of a distribution function f(A, B, x, t) defined on a 9+1D phase space, where A and B are the correlation vectors of right- and left-moving waves. We derive a transport equation (an analogous to…

Cosmological evolution of axionic strings is investigated by numerically solving field equations of a complex scalar field in 3+1 dimensions. It is shown that the global strings relax to the scaling solution with a significantly smaller…

A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions. We generalize this concept to a system of extended objects, such as strings and…

We use large-scale numerical simulations to study the formation and evolution of non-topological defects in a generalized electroweak phase transition described by the Glashow-Salam-Weinberg model without fermions. Such defects include…

We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method.…

In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there…

We examine current-carrying configurations of cosmic strings in non-Abelian gauge theories. We study the solutions numerically and point out that the currents will be at best dynamically stable and not subject to any topological…

We use the Velocity-dependent One Scale Model for topological defect evolution to explore and classify the possible scaling solutions for string networks with time-varying tension, in cosmological and non-cosmological settings and under two…

Partial synchronization is characteristic phase dynamics of coupled oscillators on various natural and artificial networks, which can remain undetected due to the complexity of the systems. With an analogy between pairwise asynchrony of…

For vortex strings in the Abelian Higgs model and D-strings in superstring theory, both of which can be regarded as cosmic strings, we give analytical study of reconnection (recombination, inter-commutation) when they collide, by using…

Configurations of vortex-strings stretched between or ending on domain walls were previously found to be 1/4 BPS states. Among zero modes of string positions, the center of mass of strings in each region between two adjacent domain walls is…

We provide a general overview of the velocity-dependent one-scale model for cosmic string evolution and discuss two further extensions to it. We introduce and justify a new ansatz for the momentum parameter $k$, and also incorporate the…