Heterogeneous network with distance dependent connectivity

Abstract.: We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtaine

Emergence of active topological glass through directed chain dynamics and nonequilibrium phase segregation

Active matter states defy many notions that have been established for systems in thermodynamic equilibrium. Nevertheless, the lack of detailed balance might be utilized to design nonequilibrium materials with unique properties. Recently we have shown, employing a model of ring polymers containing segments with a larger mobility than given by equilibrium thermal fluctuations, that making polymers with intrinsic topology active can result in states that relax extremely slowly, the so-called active topological glass. In this paper, we focus on the role of nonequilibrium phase separation in the vitrification process. In particular, we detail the polymer dynamics and show that such activity-driven glassy states arise from heterogeneity of segmental dynamics that emerges on all scales. Provided that the activity quench is strong enough, the rings feature an oriented reptationlike motion, with the active segment serving as an effective chain's end, resulting into a dramatic increase of inter-ring treading that vitrifies the system. The scaling properties of the ensuing steady-state ring conformations, which are significantly elongated and usually possess a doubly folded structure, are discussed and compared to equilibrium counterparts. We further examine the connection between the glass formation and the nonequilibrium phase separation and we find that both appear to be initiated by the contrasting dynamics of ring segments. Finally, we consider the effect of nonequilibrium phase separation in other active copolymer architectures

Active Topological Glass Confined within a Spherical Cavity

[Image: see text] We study active topological glass under spherical confinement, allowing us to exceed the chain lengths simulated previously and determine the critical exponents of the arrested conformations. We find a previously unresolved “tank-treading” dynamic mode of active segments along the ring contour. This mode can enhance active–passive phase separation in the state of active topological glass when both diffusional and conformational relaxation of the rings are significantly suppressed. Within the observational time, we see no systematic trends in the positioning of the separated active domains within the confining sphere. The arrested state exhibits coherent stochastic rotations. We discuss possible connections of the conformational and dynamic features of the system to chromosomes enclosed in the nucleus of a living cell

Heterogeneous network with distance dependent connectivity

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtained.Comment: 6 pages, 4 figures, minor clarifications and references adde

Interfacial Properties of Active-Passive Polymer Mixtures

Active matter consists of particles that dissipate energy, from their own sources, in the form of mechanical work on their surroundings. Recent interest in active-passive polymer mixtures has been driven by their relevance in phase separation of (e.g., transcriptionally) active and inactive (transcriptionally silent) DNA strands in nuclei of living cells. In this paper, we study the interfacial properties of the phase separated steady states of the active-passive polymer mixtures and compare them with equilibrium phase separation. We model the active constituents by assigning them stronger-than-thermal fluctuations. We demonstrate that the entropy production is an accurate indicator of the phase transition. We then construct phase diagrams and analyze kinetic properties of the particles as a function of the distance from the interface. Studying the interface fluctuations, we find that they follow the capillary waves spectrum. This allows us to establish a mechanistic definition of the interfacial stiffness and its dependence on the relative level of activity with respect to the passive constituents. We show how the interfacial width depends on the activity ratio and comment on the finite size effects. Our results highlight similarities and differences of the non-equilibrium steady states with an equilibrium phase separated polymer mixture with a lower critical solution temperature. We present several directions in which the non-equilibrium system can be studied further and point out interesting observations that indicate general principles behind the non-equilibrium phase separation

Small Activity Differences Drive Phase Separation in Active-Passive Polymer Mixtures

Recent theoretical studies found that mixtures of active and passive colloidal particles phase separate but only at very high activity ratio. The high value poses serious obstacles for experimental exploration of this phenomenon. Here we show using simulations that when the active and passive particles are polymers, the critical activity ratio decreases with the polymer length. This not only facilitates the experiments but also has implications on the DNA organization in living cell nuclei. Entropy production can be used as an accurate indicator of this non-equilibrium phase transition