Related papers: Stabilization of localized structures by inhomogen…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
Optical frequency comb (OFC) technology has been the cornerstone for scientific breakthroughs such as precision frequency metrology, redefinition of time, extreme light-matter interaction, and attosecond sciences. While the current…
We analyze the stability and bifurcation structure of steady states in a mechanochemical model of pattern formation in regenerating tissue spheroids. The model couples morphogen dynamics with tissue mechanics via a positive feedback loop:…
We demonstrate a new technique for the experimental measurement of the spectral coherence of microresonator optical frequency combs. Specifically, we use a spectral interference method, typically used in the context of supercontinuum…
We uncover a novel and robust phenomenon that causes the gradual self-replication of spatiotemporal Kerr cavity patterns in cylindrical microresonators. These patterns are inherently synchronised multi-frequency combs. Under proper…
We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media. We discover that under proper conditions the combination of nonlocality and vectorial coupling has a remarkable stabilizing action on multi-humped solitons. In…
Phonon localization is a phenomenon that influences numerous material properties in condensed matter physics. Anderson localization brings rise to localized atomic-scale phonon interferences in disordered lattices with an influence limited…
Machine learning techniques, such as deep learning and ensemble methods, are widely used in various domains due to their ability to handle complex real-world tasks. However, their black-box nature has raised multiple concerns about the…
This study demonstrates the realization of localized in-plane optomechanical microcavities embedded within an electrostatic MEMS architecture. The system consists of a curved, clamped-clamped microbeam, fabricated on a silicon-on-insulator…
Token representations influence the efficiency and adaptability of language models, yet conventional tokenization strategies impose rigid segmentation boundaries that do not adjust dynamically to evolving contextual relationships. The…
We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pumping. In particular, we report on the excitability regime that cavity…
Nonlinearity provides a powerful mechanism for controlling energy localization in structured dynamical systems. In this study, we investigate the emergence of nonlinearity-induced energy localization at the corners of a kagome lattice model…
Networks of coupled Kerr parametric oscillators (KPOs) hold promise as for the realization of neuromorphic and quantum computation. Yet, their rich bifurcation structure remains largely not understood. Here, we employ secular perturbation…
We study dynamical response of a nonlinear dimer to a symmetrically injected monochromatic wave. We find a domain in the space of frequency and amplitude of the injected wave where all stationary solutions are unstable. In this domain…
This research investigates dynamic response of tunable periodic structures and homogenization methods in magnetoelastic composites (MECs). The research on tunable periodic structures is focused on the design, modeling and understanding of…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
We present a stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the anomalous dispersion regime. This article is the second part of a research work whose first…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…