Related papers: Dynamics of domain wall networks with junctions
Discrete symmetries are commonplace in field theoretical models but pose a severe problem for cosmology since they lead to the formation of domain walls during spontaneous symmetry breaking in the early universe. However if one of the…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamical behavior. Even though adaptivity can improve…
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…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
We consider the possibility that current hints of spatial variations of the fine structure constant at high redshift, based on VLT/UVES and Keck/HIRES observations, could be caused by a biased domain wall network described by a scalar field…
We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…
We have analyzed a $U(1)$ model which is broken explicitly to a $Z_2$ model. The model results in generating two stable domain walls, in contrast with the more common $N_{DW}=1$ version which is prevalently used to explain axion…
We study the cosmological evolution of domain walls bounded by strings which arise naturally in axion models. If we introduce a bias in the potential, walls become metastable and finally disappear. We perform two dimensional lattice…
Numerous complex systems, both natural and artificial, are characterized by the presence of intertwined supply and/or drainage networks. Here we present a minimalist model of such co-evolving networks in a spatially continuous domain, where…
Non-equilibrium phase transitions of a scalar field in an expanding spacetime are discussed. These transitions are shown to lead, for appropriate potential energy functions, to a biased choice of vacuum structure which can be analytically…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries.…
Mostly acyclic directed networks, treated mathematically as directed graphs, arise in machine learning, biology, social science, physics, and other applications. Newman [1] has noted the mathematical challenges of such networks. In this…
We study the dynamics of domain walls in a double-field model in which the U(1) symmetry is broken both spontaneously and explicitly. The global U(1) symmetry of the system is restored when the symmetry breaking parameter $\epsilon$ is set…
We study the effects of spatial constraints on the structural properties of networks embedded in one or two dimensional space. When nodes are embedded in space, they have a well defined Euclidean distance $r$ between any pair. We assume…
Understanding the evolution and cosmological consequences of topological defect networks requires a combination of analytic modeling and numerical simulations. The canonical analytic model for defect network evolution is the…
The Two Higgs Doublet Model predicts the emergence of 3 distinct domain wall solutions arising from the breaking of 3 accidental global symmetries, $Z_2$, CP1 and CP2, at the electroweak scale for specific choices of the model parameters.…
Domain wall networks in the early universe, formed upon spontaneous breaking of a discrete symmetry, have a rich impact on cosmology. Yet, they remain somewhat unexplored. We introduce a new analytic strategy to understand better the domain…