Related papers: Understanding Domain Wall Network Evolution
The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling of the size of the domains deduced from…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
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…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
The cosmological evolution of topological defect networks can broadly be divided into two stages. At early times they are friction-dominated due to particle scattering and therefore non-relativistic, and may either be conformally stretched…
Recently spatial as well as temporal variations of the fine structure constant alpha have been reported. We show that a "runaway domain wall", which arises for the scalar field potential without minima, can account for such variations…
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on \textit{collinear dynamical systems} and their variations are…
Domain wall networks are studied in N=2 supersymmetric U(N_C) gauge theory with N_F (>N_C) flavors. We find a systematic method to construct domain wall networks in terms of moduli matrices. Normalizable moduli parameters of the network are…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
We study domain walls (DWs) arising in field theories where $Z_2$-symmetry is spontaneously broken by a scalar expectation value decreasing proportionally to the Universe temperature. The energy density of such melting DWs redshifts…
The pinning phenomena of the domain wall in the presence of exchange bias is studied analytically. The analytic solution of the domain wall spin configuration is presented. Unlike the traditional solution which is symmetric, our new…
Domain walls are the simplest type of topological defects formed at cosmological phase transitions, and one of the most constrained. Their studies typically assume a quartic double well potential, but this model is not fully representative…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…
A recent study has shown that domain walls with inflationary initial fluctuations exhibit remarkable stability against population bias due to long-range correlations, challenging the claims of prior research. In this paper, we study the…
Dynamic optimisation occurs in a variety of real-world problems. To tackle these problems, evolutionary algorithms have been extensively used due to their effectiveness and minimum design effort. However, for dynamic problems, extra…
According to the modern cosmological paradigm galaxies and galaxy systems form from tiny density perturbations generated during the very early phase of the evolution of the Universe. Using numerical simulations we study the evolution of…
Scalar field dynamics may give rise to a nonzero cosmological variation of fundamental constants. Within different scenarios based on the unification of gauge couplings, the various claimed observations and bounds may be combined in order…
Evolving Neural Networks (NNs) has recently seen an increasing interest as an alternative path that might be more successful. It has many advantages compared to other approaches, such as learning the architecture of the NNs. However, the…