Related papers: Dynamics of domain wall networks with junctions
Many dynamic networks coming from real-world contexts are link streams, i.e. a finite collection of triplets $(u,v,t)$ where $u$ and $v$ are two nodes having a link between them at time $t$. A very large number of studies on these objects…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives rise to nonlocal evolution equations on fractal domains.…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resulting dynamics are typically…
The dynamics of a domain wall in magnetostrictive materials is investigated. The domain wall is modeled by a d-dimensional interface moving in a d+1-dimensional environment. Long-range demagnetization effects and quenched disorder are…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional…
The spontaneous breaking of a discrete symmetry can lead to the formation of domain walls in the early Universe. In this work, we explore the impact of bias directions on the dynamics of $Z_N$ domain walls, mainly focusing on the $N = 3$…
Domain walls form at phase transitions which break discrete symmetries. In a cosmological context they often overclose the universe (contrary to observational evidence), although one may prevent this by introducing biases or forcing…
Motivated by the well know Chamblin-Reall solutions of $n$-dimensional background spacetime in a dilaton gravity and the dynamics of a domain wall in the same backgrounds, we have tried to generalize those solutions by including…
We propose noncanonical domain walls as a new dark energy model inspired by grand unified theories (GUTs). We investigate the cosmic dynamics and discover that the domain walls act as either dark energy or dark matter at different times,…
We explore the idea of a network of domain walls to appear at the surface of a soliton star. We show that for a suitable fine tuning among the parameters of the model we can find localized fermion zero modes only on the network of domain…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the…
We revisit the velocity-dependent one-scale model for topological defect evolution, and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale. While the two approaches are…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…