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We investigate the formation of localized structures with a varying width in one and two-dimensional systems. The mechanism of stabilization is attributed to strong nonlocal coupling mediated by a Lorentzian type of Kernel. We show that, in…
We study the dynamics of (synchronous) one-dimensional cellular automata with cyclical boundary conditions that evolve according to the majority rule with radius $ r $. We introduce a notion that we term cell stability with which we express…
We study the regularity of segregated profiles arising from competition - diffusion models, where the diffusion process is of nonlocal type and is driven by the fractional Laplacian of power $s \in (0,1)$. Among others, our results apply to…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
Spontaneous stratification of granular mixtures has been reported by Makse et al. [Nature 386, 379 (1997)] when a mixture of grains differing in size and shape is poured in a quasi-two-dimensional heap. We study this phenomenon using two…
Using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one…
Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…
We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions…
We study quantum dynamics of a wave packet on a class of one dimensional decorated aperiodic lattices, described within a tight binding formalism. We look for the possibility of finding extended single particle states even in the absence of…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
I investigate models with scalar fields in 5 dimensions that exhibit thick-brane configurations with a non-trivial metric. I show that an appropriate coupling to the scalar curvature allows for periodic configurations, which, however, are…
Periodic fluidization of solids in a gas medium can generate structured bubbling patterns. This phenomenon has been successfully reproduced in fluidized bed systems called pulsed-fluidized beds, known for their efficient mixing and…
We study the abelian sandpile model in two dimensions on a directed cylindrical lattice with periodic transverse boundary conditions in the transverse direction and dissipation at one boundary. Recurrent configurations form a finite abelian…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Discrete breathers with purely anharmonic short-range interaction potentials localize super-exponentially becoming compact-like. We analyze their spatial localization properties and their dynamical stability. Several branches of solutions…
Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mutual local derivability class of the Penrose tiling, as well…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of…