Related papers: Ordering Dynamics of Topological Defect Networks
We have studied the cosmological evolution of domain wall networks in two, three and four spatial dimensions using high-resolution field theory simulations. The dynamical range and number of our simulations is larger than in previous works,…
We study the evolution of domain wall networks appearing after phase transitions in the early Universe. They exhibit interesting dynamical scaling behaviour which is not yet well understood, and are also simple models for the more…
Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…
Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…
An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However,…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
Numerical simulations of phase ordering under dissipative dynamics in a (2+1)-dimensional 3-vector model with O(3) symmetry are reported. The energy functional includes terms which stabilize the size of extended topological defects. They…
The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…
Topological data analysis (TDA) allows us to explore the topological features of a dataset. Among topological features, lower dimensional ones have recently drawn the attention of practitioners in mathematics and statistics due to their…
The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer…
The presence of defects in material continua is known to produce internal permanent strained states. Extending the theory of defects to four dimensions and allowing for the appropriate signature, it is possible to apply these concepts to…
In this paper we show that a universe dominated by two components, namely domain walls and dissipative dark matter such that the former slowly decays into the latter may drive power law cosmological acceleration consistent with the high…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…
We study the dynamics of a cosmological bubble wall beyond the approximation of an infinitely thin wall. In a previous paper, we discussed the range of validity of this approximation and estimated the first-order corrections due to the…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
With the latest advances in Deep Learning-based generative models, it has not taken long to take advantage of their remarkable performance in the area of time series. Deep neural networks used to work with time series heavily depend on the…