Rodlike localized structure in isotropic pattern-forming systems

Bordeu, Ignacio; Clerc, Marcel G.

doi:10.1103/physreve.92.042915

Cited by 11 publications

(6 citation statements)

References 52 publications

(61 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have found no evidence for the coexistence of this state with any spatially extended state at these parameter values. Note that dumbbell localized states were previously observed in the classical nonconserved SH equation in both 2D and 3D [112]. Next, we move on to the active PFC model and investigate the influence of the activity parameter v 0 .…”

Section: Localized Statesmentioning

confidence: 92%

Two-dimensional localized states in an active phase-field-crystal model

et al. 2021

View full text Add to dashboard Cite

The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and aspects of the Toner-Tu theory for self-propelled particles. We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions. Due to the activity, crystalline states can undergo a drift instability and start to travel while keeping their spatial structure. Based on linear stability analyses, time simulations and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of resting and traveling states. We explore, for instance, how the slanted homoclinic snaking of steady localized states found for the passive PFC model is modified by activity. The analysis is carried out for the model in two spatial dimensions. Morphological phase diagrams showing the regions of existence of various solution types are presented merging the results from all the analysis tools employed. We also study how activity influences the crystal structure with transitions from hexagons to rhombic and stripe patterns. This in-depth analysis of a simple PFC model for active crystals and swarm formation provides a clear general understanding of the observed multistability and associated hysteresis effects, and identifies thresholds for qualitative changes in behavior.

show abstract

Section: Localized Statesmentioning

confidence: 92%

Two-dimensional localized states in an active phase-field-crystal model

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Figure 3 depicts the bifurcation diagram of Eq. (2) as function of the parameter η (for details of the bifurcation diagram see refs 22,24,27 ). The vertical axis accounts for the amplitude || A || of the pattern.…”

Section: Resultsmentioning

confidence: 99%

Extended stable equilibrium invaded by an unstable state

Castillo-Pinto

Clerc

González-Cortés

2019

Sci Rep

Self Cite

View full text Add to dashboard Cite

Coexistence of states is an indispensable feature in the observation of domain walls, interfaces, shock waves or fronts in macroscopic systems. The propagation of these nonlinear waves depends on the relative stability of the connected equilibria. In particular, one expects a stable equilibrium to invade an unstable one, such as occur in combustion, in the spread of permanent contagious diseases, or in the freezing of supercooled water. Here, we show that an unstable state generically can invade a locally stable one in the context of the pattern forming systems. The origin of this phenomenon is related to the lower energy unstable state invading the locally stable but higher energy state. Based on a one-dimensional model we reveal the necessary features to observe this phenomenon. This scenario is fulfilled in the case of a first order spatial instability. A photo-isomerization experiment of a dye-dopant nematic liquid crystal, allow us to observe the front propagation from an unstable state.

show abstract

“…Several physical effect have been proposed in the literature such as Kerr cavities [17][18][19] . The existence of stable LBs have been reported in other systems such as in wide-aperture lasers with a saturable absorber [20][21][22][23][24] , optical parametric oscillators [25][26][27] , second harmonic generation [28,29] , passively mode-locked semiconductor lasers [30] , left-handed materials [31] , twisted waveguide arrays [32] , in Swif-Hohenberg equation [25,28,33] , and in the complex cubic-quintic Ginzburg-Landau equation [34] . (see recent reviews [35][36][37] ).…”

Section: Introductionmentioning

confidence: 95%

Optical crystals and light-bullets in Kerr resonators

Tlidi

Gopalakrishnan

Taki

et al. 2021

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

show abstract

Rodlike localized structure in isotropic pattern-forming systems

Cited by 11 publications

References 52 publications

Two-dimensional localized states in an active phase-field-crystal model

Two-dimensional localized states in an active phase-field-crystal model

Extended stable equilibrium invaded by an unstable state

Optical crystals and light-bullets in Kerr resonators

Contact Info

Product

Resources

About