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This thesis discusses the full scope of a project exploring the physics of hierarchical clusters of interacting nanomagnets. These clusters may be relevant for novel applications such as multilevel da...
Oscillatory critical amplitudes have been repeatedly observed in hierarchical models and, in the cases that have been taken into consideration, these oscillations are so small to be hardly detectable....
Recently, some studies have revealed that non-Poissonian statistics of human behaviors stem from the hierarchical geographical network structure. On this view, we focus on epidemic spreading in the hi...
We study the role of hierarchical structures in a simple model of collective consensus formation based on the bounded confidence model with continuous individual opinions. For the particular variation...
Abstract: In this paper, we study many geometrical properties of the contour loops to characterize the morphology of typical synthetic multifractal surfaces following multiplicative hierarchical casca...
Abstract: General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations fo...
Motif based hierarchical random graphs: structural properties and critical points of an Ising model.
A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D....
Abstract: An adiabatic cycle of parameters in a quantum system can yield the quantum anholonomies, nontrivial evolution not just in phase of the states, but also in eigenvalues and eigenstates. Such e...
The model of community isolation was extended to the case when individuals are randomly placed at nodes of hierarchical modular networks. It was shown that the average number of blocked nodes (individ...
The Earth's surface is subdivided into eight large tectonic plates and many smaller ones. We reconstruct the plate tessellation history and demonstrate that both large and small plates display two di...
We study a random code ensemble with a hierarchical structure, which is closely related to generalized random energy model with discrete energy values.Based on this correspondence, we analyze this ens...
On a lattice with equal spacing on the logarithmic scale, a momentum operator that respects the asymmetry of this nonlinear lattice yields a kinetics that can be understood in terms of diffusion on an...
We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hillard equation. The evolution leads to a fractalization into small...

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