Related papers: Physical and invariant models for defect network e…
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 investigate the interplay between disorder and superconducting pairing for a one-dimensional $p$-wave superconductor subject to slowly varying incommensurate potentials with mobility edges. With amplitude increments of the incommensurate…
Nonequilibrium states of quantum materials can exhibit exotic properties and enable unprecedented functionality and applications. These transient states are inherently inhomogeneous, characterized by the formation of topologically protected…
Recent experiments began to explore the topological properties of quench dynamics, i.e. the time evolution following a sudden change in the Hamiltonian, via tomography of quantum gases in optical lattices. In contrast to the well…
The structure of the divergences for transverse theories of gravity is studied to one-loop order. These theories are invariant only under those diffeomorphisms that enjoy unit Jacobian determinant (TDiff), so that the determinant of the…
The genus of the iso-density contours is a robust measure of the topology of large scale structure, and it is relatively insensitive to nonlinear gravitational evolution, galaxy bias and redshift-space distortion. We show that the growth of…
The topological properties of a material depend on its symmetries, parameters, and spatial dimension. Changes in these properties due to parameter and symmetry variations can be understood by computing the corresponding topological…
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
Cosmic strings are topological defects arising in a variety of cosmological scenarios, as the Universe undergoes symmetry-breaking phase transitions, whose discovery would offer valuable insight into the high-energy physics that shaped the…
The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic…
This article examines the cosmic evolution in the framework of symmetric teleparallel theory, characterized by the function of non-metricity scalar $(\mathcal{Q})$. We use the e-folding number and reconstruction method with a suitable…
The rate at which nodes in evolving social networks acquire links (friends, citations) shows complex temporal dynamics. Preferential attachment and link copying models, while enabling elegant analysis, only capture rich-gets-richer effects,…
We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
We present a gauge-invariant formalism to study the evolution of curvature perturbations in a Friedmann-Robertson-Walker universe filled by multiple interacting fluids. We resolve arbitrary perturbations into adiabatic and entropy…
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,…
We study the evolution of the graph distance and weighted distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with power-law exponent $\tau\in(2,3)$,…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
I use a combination of state-of-the-art numerical simulations and analytic modelling to discuss the scaling properties of cosmic defect networks, including superstrings. Particular attention is given to the role of extra degrees of freedom…