Related papers: Dynamics of Influence on Hierarchical Structures
The hierarchical topology is a common property of many complex systems. Here we introduce a simple but generic model of hierarchy growth from the bottom to the top. Therein, two dynamical processes are accounted for: agent's promotions to…
A lattice system of spinor atoms or molecules experiencing quadratic Zeeman effect is considered. This can be an optical lattice with sufficiently deep wells at lattice sites, so that the system is in an isolating state, where atoms are…
In this paper we consider models with nearest-neighbor interactions and with the set [0,1] of spin values, on a Bethe lattice (Cayley tree) of an arbitrary order. These models depend on parameter $\theta$. We describe all of Gibbs measures…
We show that a system of spinless Fermi particles, localized on the sites of the Bethe lattice with coordination number z and interacting through a repulsive nearest-neighbor interaction, exhibits a phase transition to a charge-ordered…
Assembly and stability of mitotic spindle is governed by the interplay of various intra-cellular forces, e.g. the forces generated by motor proteins by sliding overlapping anti-parallel microtubules (MTs) polymerized from the opposite…
We introduce and solve analytically a model for the development of disparate social classes in a competitive population. Individuals advance their fitness by competing against those in lower classes, and in parallel, individuals decline due…
Decisions to pursue higher education are not fully explained by economic incentives, with social influence and peer effects playing a crucial, yet dynamically understudied, role. This paper develops a theoretical non-linear dynamics model…
In this paper, we study the topological properties of magnons on a dice lattice, also known as the dual of a more widely studied kagome lattice. This structure has a central atom at the center of the honeycomb lattice, which leads to the…
We investigate the dynamical properties of the classical antiferromagnetic Heisenberg model on the kagome lattice using a combination of Monte Carlo and molecular dynamics simulations. We find that frustration induces a distribution of…
We study metastability for Glauber spin-flip dynamics on the $N$-dimensional hierarchical lattice with $n$ hierarchical levels. Each vertex carries an Ising spin that can take the values $-1$ or $+1$. Spins interact with an external…
The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This…
We give a general condition for a discrete spin system with nearest-neighbor interactions on the $\mathbb{Z}^d$ lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order…
We show that atomic dipolar effects are detectable in the system that recently demonstrated two-atom coherent spin dynamics within individual lattice sites of a Mott state. Based on a two-state approximation for the two-atom internal states…
We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the Majority Rule, applied…
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…
The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both…
In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis…
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation. If the…
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…
Magnetic materials play a key role in the contemporary industry, providing unique features with a wide application potential. To study physical phenomena and design new materials, it is important to possess an appropriate tool, a model…