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Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has…
We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number $m+1 = 3$, with a box distribution of…
We study the thermalization properties of a fully nonlinear lattice model originally derived from the two-dimensional cubic defocusing nonlinear Schr\"odinger equation (NLS) using analytical and numerical methods. Our analysis reveals both…
Wave motion is fundamentally constrained by the dispersion properties of the medium, often making it challenging -- or even impossible -- to guide wave packets along desired trajectories, particularly when wave inversion is required. The…
We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear…
We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes, gap solitons and truncated nonlinear Bloch waves, in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity,…
We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking…
We investigate the quantum dynamics of wave packets in a class of decorated lattices, both quasiperiodic and random, where a nominal quasi-one dimensionality is introduced at local levels, bringing in a deterministic or even random…
A model Hamiltonian is proposed in order to understand the localization-delocalization transition in a quantum dot, where there are two gate voltages: top and side. Considering energetically favorable degrees of freedom only, we achieve a…
We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic…
We examine quantum decay of localized vibrations in anharmonic crystal lattice. The theory which describes two-phonon anharmonic relaxation can be applied both to local modes associated with substitutional impurity and to intrinsic local…
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation…
We predict that photonic moir\'e lattices produced by two mutually twisted periodic sublattices in the medium with Kerr nonlinearity can support stable three-dimensional light bullets localized in both space and time. Stability of light…
Linear and nonlinear energy optimizations in a tilted domain are used to unveil the main mechanisms allowing the creation of a turbulent band in a channel flow. Linear optimization predicts an optimal growth for streamwse and spanwise…
We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a…
Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical…
Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one…
In a previous work [Dillon and Nakanishi, Eur. Phys.J B {\bf 87}, 286 (2014)], we calculated the transmission coefficient of the two-dimensional quantum percolation model and found there to be three regimes, namely, exponentially localized,…
Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor.…
We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which…