Related papers: Understanding Domain Wall Network Evolution
Cosmological domain walls appear in many well-motivated extensions to the standard model of particle physics. If produced, they quickly enter into a self-similar scaling regime, where they are capable of efficiently sourcing a stochastic…
In this paper, we address the problem of dynamic network embedding, that is, representing the nodes of a dynamic network as evolving vectors within a low-dimensional space. While the field of static network embedding is wide and…
Experimental measurements of domain wall propagation are typically interpreted by comparison to reduced models that ignore both the effects of disorder and the internal dynamics of the domain wall structure. Using micromagnetic simulations,…
We have investigated the dynamics of domain walls in the cubic anisotropy model. In this model a global O(N) symmetry is broken to a set of discrete vacua either on the faces, or vertices of a (hyper)cube. We compute the scaling exponents…
We classify the cosmological behaviors of the domain wall under junctions between two spacetimes in terms of various parameters: cosmological constants of bulk spacetime, a tension of a domain wall, and mass parameters of the black…
In this contribution, we discuss the cosmological scenario where unstable domain walls are formed in the early universe and their late-time annihilation produces a significant amount of gravitational waves. After describing cosmological…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…
A family of degenerate domain wall configurations, partially preserving supersymmetry, is discussed in a generalized Wess-Zumino model with two scalar superfields. We establish some general features inherent to the models with continuously…
Domain wall networks on the surface of a soliton are studied in a simple theory. It consists of two complex scalar fields, in (3+1)-dimensions, with a global U(1) x Z_n symmetry, where n>2. Solutions are computed numerically in which one of…
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…
The geometry and morphology of magnetic domain walls (DWs) are closely related to their dynamics when driven by external forces. Under some reliable approximations DWs can be considered self-affine interfaces, so universal laws govern their…
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…
Modeling human dynamics responsible for the formation and evolution of the so-called social networks - structures comprised of individuals or organizations and indicating connectivities existing in a community - is a topic recently…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
We study a fundamental issue in cosmology: Whether we can rely on a cosmological model to understand the real history of the Universe. This fundamental, still unresolved issue is often called the ``model-fitting problem (or averaging…
In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
Air transport systems are highly dynamic at temporal scales from minutes to years. This dynamic behavior not only characterizes the evolution of the system but also affect the system's functioning. Understanding the evolutionary mechanisms…
We study a coupled dynamics of a network and a particle system. Particles of density $\rho$ diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics…