Related papers: Fractal globule as an artificial molecular machine

Many organisms have an elastic skeleton that consists of a closed shell of epithelial cells that is filled with fluid, and can actively regulate both elastic forces in the shell and hydrostatic pressure inside it. In this work we introduce…

We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to an extensional force We show that with an increase in the applied force…

We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…

Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…

The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…

We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to extensional deformation. We demonstrate that depending on the degree of…

Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…

Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…

We investigate the internal structure of a polymer during collapse from an expanded coil to a compact globule. Collapse is more probable in local regions of high curvature, so a smoothing of the fractal polymer structure occurs that…

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the…

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting…

By simulating the first order globule-crystal transition of a flexible homopolymer chain, both by collision dynamics and Monte Carlo with non-kinetic moves, we show that the effective and the thermodynamic transition temperatures are…

The mechanical properties of thermally excited two-dimensional crystalline membranes can depend dramatically on their geometry and topology. A particularly relevant example is the effect on the crumpling transition of holes in the membrane.…

Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems raging from the brain to high-order social networks.…

Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have…

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…

If quenched fast enough, a liquid is able to avoid crystallization and will remain in a metastable supercooled state down to the glass transition, with an important increase in viscosity upon further cooling. There are important differences…

In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…