Related papers: Stabilization of localized structures by inhomogen…
A driven resonator with focusing Kerr nonlinearity shows stable localized structures in a region far from modulational instability. The stabilization mechanism is based on front interaction in bistable regime with an inhomogeneous injected…
Understanding how atomic-level structures govern the mechanical properties of amorphous materials remains a fundamental challenge in solid-state physics. Under mechanical loading, amorphous materials exhibit simple affine and spatially…
Dissipative soliton Kerr frequency combs in microresonators have recently been demonstrated with the self-injection locking process. They have the advantage of turnkey deterministic comb generation and simplifying dark soliton generation in…
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…
With demonstrated applications ranging from metrology to telecommunications, soliton microresonator frequency combs have emerged over the past decade as a remarkable new technology. However, standard implementations only allow for the…
Kerr frequency combs generated from microresonators are the subject of intense study. Most research employs microresonators with anomalous dispersion, for which modulation instability is believed to play a key role in initiation of the…
Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bends{\o}e and Kikuchi from 1988, which…
Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
We study the dynamics and stability of soliton optical frequency comb generation in a dissipative, coherently pumped cavity with both second and third-order nonlinearity. Cavity sweep simulations and linear stability analysis based on path…
We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the…
We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, "hat-like" spatial inhomogeneity. The spatial inhomogeneity corresponds to a spatially dependent scaling of the sine-Gordon…
Kerr optical frequency combs generated in a coherently driven Kerr nonlinear resonator has the potential for a wide range of applications. However, in a single cavity which is a widely adopted configuration for Kerr optical frequency combs…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
In this letter we theoretically investigate the formation of localized temporal dissipative structures, and their corresponding frequency combs in doubly resonant dispersive optical parametric oscillators. We derive a nonlocal mean field…
This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the recently proposed sparsifying preconditioner with two major…
The emergence of localised vibrations in cyclic and symmetric rotating structures, such as bladed disks of aircraft engines, has challenged engineers in the past few decades. In the linear regime, localised states may arise due to a lack of…
The local stability of stellar and fluid discs, under a new modified dynamical model, is surveyed by using WKB approximation. The exact form of the modified Toomre criterion is derived for both types of systems and it is shown that the new…