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The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact…
We numerically investigate the aging dynamics of a monatomic Lennard-Jones glass, focusing on the topology of the potential energy landscape which, to this aim, has been partitioned in basins of attraction of stationary points (saddles and…
Aging behavior is an important effect in the friction properties of solid surfaces. In this paper we investigate the temporal evolution of the static properties of a granular medium by studying the aging over time of the maximum stability…
Aging in an attraction-driven colloidal glass is studied by computer simulations. The system is equilibrated without attraction and instantaneously ``quenched'', at constant colloid volume fraction, to one of two states beyond the glass…
A few recent papers introduced the concept of topological synchronisation. We refer in particular to \cite{TS}, where the theory was illustrated by means of a skew product system, coupling two logistic maps. In this case, we show that the…
We construct the equations for the growth kinetics of an aging structural glass within mode-coupling theory through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. {\bf 97}, 195701 (2006). We solve a…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
Living systems are subject to the arrow of time; from birth, they undergo complex transformations (self-organization) in a constant battle for survival, but inevitably ageing and disease trap them to death. Can ageing be understood and…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at…
We study concentrated colloidal suspensions, a model system which has a glass transition. The non-equilibrium nature of the glassy state is most clearly highlighted by aging -- the dependence of the system's properties on the time elapsed…
Complex spatiotemporal structures develop during the process of aging glasses after cooling and of rejuvenating glasses upon heating. The key to understanding these structures is the interplay between the activated reconfiguration events…
New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from…
We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display non-local entanglement. To this end, we introduce and study a…
We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle -- a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape…
Understanding glasses is considered to be one of the most fundamental problems in statistical physics. A theoretical approach to unravel their universal properties is to consider the validity of equilibrium concepts such as temperature and…