Related papers: Ordering Dynamics of Topological Defect Networks
We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle…
We apply the formalism of dynamical system analysis to investigate the evolution of interacting dark energy scenarios at the background and perturbation levels in a unified way. Since the resulting dynamical system contains the extra…
We introduce a new phenomenological one-scale model for the evolution of domain wall networks, and test it against high-resolution field theory numerical simulations. We argue that previous numerical estimates of wall velocities are…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
Density estimation is a versatile technique underlying many data mining tasks and techniques,ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
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…
Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
My research focuses on the analysis, recovery, and generation of 4D content, where 4D includes three spatial dimensions (x, y, z) and a temporal dimension t, such as shape and motion. This focus goes beyond static objects to include dynamic…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Exact string solutions are presented, providing backgrounds where a dynamical change of topology is occuring. This is induced by the time variation of a modulus field. Some lessons are drawn concerning the region of validity of effective…
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…
We use numerical simulations of the time evolution of global textures to investigate the relationship between ordering dynamics and energy density in an expanding universe. Events in which individual textures become fully wound are rare.…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
Previous work developed a space-time metric with two cosmological scales; one that conveniently describes the classical evolution of the dynamics, and the other describing a scale associated with macroscopic quantum aspects like vacuum…
The persistent dynamics in systems out of equilibrium, particularly those characterized by annihilation and creation of topological defects, is known to involve complicated spatiotemporal processes and is deemed difficult to control. Here…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…