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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.18736808 |
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| _version_ | 1866901725315596288 |
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| author | Chávez Juárez, Gerardo Azahél |
| author_facet | Chávez Juárez, Gerardo Azahél |
| contents | <p>A three-dimensional reduced model is presented describing the interaction <br>between a dominant flow mode (Galerkin projection of the Stokes problem) <br>and two structural variables: the coherence λ(t) and the structural <br>feedback force σ(t). The system analytically captures the spontaneous <br>emergence of coherent structures through saddle-node bifurcations and <br>possible Hopf bifurcations. The stationary points, the transcendental <br>equilibrium equation, the full Jacobian, the cubic characteristic <br>polynomial, and the exact Routh–Hurwitz conditions for asymptotic <br>stability are explicitly derived. The origin is unstable when the <br>structural force is autocatalytic (γ > 0), enabling self-organization. The <br>dimensionless form of the system and a qualitative analysis of the <br>dynamical regimes are included. The framework is applicable to <br>viscoelastic fluids, biological active fluids, and elastic turbulence. </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18736808 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Self-Organization and Bifurcations in Coherent Flows Chávez Juárez, Gerardo Azahél <p>A three-dimensional reduced model is presented describing the interaction <br>between a dominant flow mode (Galerkin projection of the Stokes problem) <br>and two structural variables: the coherence λ(t) and the structural <br>feedback force σ(t). The system analytically captures the spontaneous <br>emergence of coherent structures through saddle-node bifurcations and <br>possible Hopf bifurcations. The stationary points, the transcendental <br>equilibrium equation, the full Jacobian, the cubic characteristic <br>polynomial, and the exact Routh–Hurwitz conditions for asymptotic <br>stability are explicitly derived. The origin is unstable when the <br>structural force is autocatalytic (γ > 0), enabling self-organization. The <br>dimensionless form of the system and a qualitative analysis of the <br>dynamical regimes are included. The framework is applicable to <br>viscoelastic fluids, biological active fluids, and elastic turbulence. </p> |
| title | Self-Organization and Bifurcations in Coherent Flows |
| url | https://doi.org/10.5281/zenodo.18736808 |