U.S. flag An official website of the United States government.
Official websites use .gov

A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS

A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

i

Bifurcation delay and front propagation in the real Ginzburg-Landau equation on a time-dependent domain



Details

  • Journal Title:
    Physical Review E
  • Personal Author:
  • NOAA Program & Office:
    Sea Grant
  • Description:
    This work analyzes bifurcation delay and front propagation in the one-dimensional real Ginzburg-Landau equation with periodic boundary conditions on isotropically growing or shrinking domains. First, we obtain closed-form expressions for the delay of primary bifurcations on a growing domain and show that the additional domain growth before the appearance of a pattern is independent of the growth time scale. We also quantify primary bifurcation delay on a shrinking domain; in contrast with a growing domain, the time scale of domain compression is reflected in the additional compression before the pattern decays. For secondary bifurcations such as the Eckhaus instability, we obtain a lower bound on the delay of phase slips due to a time-dependent domain. We also construct a heuristic model to classify regimes with arrested phase slips, i.e., phase slips that fail to develop. Then, we study how propagating fronts are influenced by a time-dependent domain. We identify three types of pulled fronts: homogeneous, pattern spreading, and Eckhaus fronts. By following the linear dynamics, we derive expressions for the velocity and profile of homogeneous fronts on a time-dependent domain. We also derive the natural “asymptotic” velocity and front profile and show that these deviate from predictions based on the marginal stability criterion familiar from fixed domain theory. This difference arises because the time dependence of the domain lifts the degeneracy of the spatial eigenvalues associated with speed selection and represents a fundamental distinction from the fixed domain theory that we verify using direct numerical simulations. The effect of a growing domain on pattern spreading and Eckhaus front velocities is inspected qualitatively and found to be similar to that of homogeneous fronts. These more complex fronts can also experience delayed onset. Lastly, we show that dilution—an effect present when the order parameter is conserved—increases bifurcation delay and amplifies changes in the homogeneous front velocity on time-dependent domains. The study provides general insight into the effects of domain growth on pattern onset, pattern transitions, and front propagation in systems across different scientific fields.
  • Source:
    Physical Review E, 109(4)
  • DOI:
  • ISSN:
    2470-0045 ; 2470-0053
  • Format:
    pdf
  • Publisher:
    American Physical Society (APS)
  • Document Type:
    Journal Article
  • Rights Information:
    Accepted Manuscript
  • Compliance:
    Submitted
  • Main Document Checksum:
    urn:sha-512:1b3f82ab34742200ccb2dab2e7d57aa0b936f81c46a1cac84e67cdd5b6a0f0ebc963ce8a9ba3c2cd61fd26fd6e8f783fe7eb34c0a244e18f4aa6ac1dd96b8ce2
  • Download URL:
  • File Type:
    Filetype[PDF - 4.25 MB ]
PREVIOUS
ON THIS PAGE
Details
The NOAA IR serves as an archival repository of NOAA-published products including scientific findings, journal articles, guidelines, recommendations, or other information authored or co-authored by NOAA or funded partners. As a repository, the NOAA IR retains documents in their original published format to ensure public access to scientific information.
BACK TO TOP