Related papers: Understanding Domain Wall Network Evolution
Randall-Sundrum model, which has a scalar field, is used to investigate the domain structure of the extra dimension and to obtain a possible solution of the mass hierarchy problem. It is found that when the domain wall size is comparable to…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
Network representations have been effectively employed to analyze complex systems across various areas and applications, leading to the development of network science as a core tool to study systems with multiple components and complex…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
We study domain walls which can be created in the Standard Model under the assumption that it is valid up to very high energy scales. We focus on domain walls interpolating between the physical electroweak vacuum and the global minimum…
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…
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…
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…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…
We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string…
Light scalar fields, with double well potentials and direct matter couplings, undergo density driven phase transitions, leading to the formation of domain walls. Such theories could explain dark energy, dark matter or source the nanoHz…
Dynamics of cylindrical and spherical relativistic domain walls is investigated with the help of a new method based on Taylor expansion of the scalar field in a vicinity of the core of the wall. Internal oscillatory modes for the domain…
With Monte Carlo methods, we investigate the relaxation dynamics of a domain wall in the two-dimensional random-field Ising model with a driving field. The short-time dynamic behavior at the depinning transition is carefully examined, and…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
We present a model for the description of the evolution of contacts among individuals in a network. At each time step each individual is associated with a domain or neighborhood of fully connected agents.The dynamics of this changing…
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
In this paper, we analyse a model for the growth of three-dimensional walled cells. In this model the biomechanical expansion of the cell is coupled with the geometry of its wall. We consider that the density of building material depends on…