Related papers: Defect Junctions and Domain Wall Dynamics
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local…
We investigate the potential role of string and monopole-type junctions in the frustration of domain wall networks using a velocity-dependent one-scale model for the characteristic velocity, $v$, and the characteristic length, $L$, of the…
We reconsider a cosmological evolution of domain walls produced by spontaneous breaking of an approxime discrete symmetry. We show, that domain walls may never collapse even if the standard bound on the vacuum energy asymmetry is satisfied.…
When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern…
We investigate several models of coupled scalar fields that present discrete Z_2, Z_2 x Z_2, Z_3 and other symmetries. These models support topological domain wall solutions of the BPS and non-BPS type. The BPS solutions are stable, but the…
One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…
We prove a local existence result for a PDE system that describes curvature motion of networks with a dynamic boundary condition known as triple junction drag. This model arises in the study of grain boundary evolution in polycrystalline…
We discuss the phenomenon of the smooth dynamical gravity induced crossing of the phantom divide line in a framework of simple cosmological models where it appears to occur rather naturally, provided the potential of the unique scalar field…
We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting…
In the first-order phase transitions (PTs) colliding bubble is an important gravitational wave (GW) source. Following bubble collision, domain walls can be formed when degenerate vacua occur as a result of the breaking of a discrete…
The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue…
We apply a recently developed analytic model for the evolution of monopole networks to the case of monopoles attached to one string, usually known as hybrid networks. We discuss scaling solutions for both local and global hybrid networks,…
A novel mechanism for the production of a cosmic network of fundamental superstrings based on a time-varying string tension has been recently proposed in the context of a kinating background driven by the volume modulus of string…
Links in a practical network may have different functions, which makes the original network a combination of some functional subnetworks. Here, by a model of coupled oscillators, we investigate how such functional subnetworks are evolved…
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…
We demonstrate that the dynamics of neural networks trained with gradient descent and the dynamics of scalar fields in a flat, vacuum energy dominated Universe are structurally profoundly related. This duality provides the framework for…
Resilience of the most important properties of stochastic and regular (deterministic) small-world interconnection networks is studied. It is shown that in the broad range of values of the fraction of faulty nodes the networks under…
The existence of cusps on non-periodic strings ending on D-branes is demonstrated and the conditions, for which such cusps are generic, are derived. The dynamics of F-, D-string and FD-string junctions are investigated. It is shown that…
We introduce novel sets of measures with the goal of describing dynamical properties of force networks in dense particulate systems. The presented approach is based on persistent homology and allows for extracting precise, quantitative…