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1. Nonlinear Rayleigh–Taylor instability of inhomogeneous incompressible geophysical fluids with partial dissipation

   https://doi.org/10.1088/1361-6544/adca80  

   Fan, Yanlong; Han, Daozhi; Wang, Quan; Xing, Chao (April 2025, Nonlinearity)

   Abstract This article examines the Rayleigh–Taylor instability in an rotating inhomogeneous, incompressible fluid with partial viscosity. First, using the modified variational method, we demonstrate the existence of an exponentially growing normal mode in $H^k,k\text{⩾}0$and establish the instability of the linearised problem. Then, we obtain a nonlinear energy estimate for the problem with small initial data. In this process, we employ an innovative method to derive energy estimates for both density and velocity, effectively addressing the challenges posed by partial viscosity. Third, we prove the existence of a classical solution forH³initial data, provided it satisfies a compatibility condition. Finally, by integrating the results of the previous steps, we establish the nonlinear instability of the system in the Hadamard sense. 

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2. Generalized stacking fault energy surface mismatch and dislocation transformation

   https://doi.org/10.1038/s41524-021-00660-z  

   Feng, Longsheng; Mills, Michael J.; Wang, Yunzhi (December 2021, npj Computational Materials)

   Abstract Even though the fundamental rules governing dislocation activities have been well established in the past century, we report a phenomenon, dislocation transformation, governed by the generalized-stacking-fault energy surface mismatch (GSF mismatch for short) between two co-existing phases. By carrying out ab-initio-informed microscopic phase-field simulations, we demonstrate that the GSF mismatch between a high symmetry matrix phase and a low symmetry precipitate phase can transform an array of identical full dislocations in the matrix into an array of two different types of full dislocations when they shear through the precipitates. The precipitates serve as a passive Shockley partial source, creating new Shockley partial dislocations that are neither the ones from the dissociation of the full dislocation. This phenomenon enriches our fundamental understanding of partial dislocation nucleation and dislocation-precipitate interactions, offering additional opportunities to tailor work-hardening and twinning processes in alloys strengthened by low-symmetry precipitate phases. 

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3. Radial symmetry of minimizers to the weighted Dirichlet energy

   https://doi.org/10.1017/prm.2020.8  

   Koski, Aleksis; Onninen, Jani (February 2020, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)

   null (Ed.)

   Abstract We consider the problem of minimizing the weighted Dirichlet energy between homeomorphisms of planar annuli. A known challenge lies in the case when the weight λ depends on the independent variable z . We prove that for an increasing radial weight λ ( z ) the infimal energy within the class of all Sobolev homeomorphisms is the same as in the class of radially symmetric maps. For a general radial weight λ ( z ) we establish the same result in the case when the target is conformally thin compared to the domain. Fixing the admissible homeomorphisms on the outer boundary we establish the radial symmetry for every such weight. 

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4. Approximation of fractional harmonic maps

   https://doi.org/10.1093/imanum/drac029  

   Antil, Harbir; Bartels, Sören; Schikorra, Armin (July 2022, IMA Journal of Numerical Analysis)

   Abstract This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet energy on unit-length vector fields. We devise and analyze numerical methods for the approximation of various partial differential equations related to fractional harmonic maps. The compactness results imply the convergence of numerical approximations. Numerical examples on spin chain dynamics and point defects are presented to demonstrate the effectiveness of the proposed methods. 

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5. A mechanical model reveals that non-axisymmetric buckling lowers the energy barrier associated with membrane neck constriction

   https://doi.org/10.1039/c9sm01494b  

   Vasan, R.; Rudraraju, S.; Akamatsu, M.; Garikipati, K.; Rangamani, P. (January 2020, Soft Matter)

   Membrane neck formation is essential for scission, which, as recent experiments on tubules have demonstrated, can be location dependent. The diversity of biological machinery that can constrict a neck such as dynamin, actin, ESCRTs and BAR proteins, and the range of forces and deflection over which they operate, suggest that the constriction process is functionally mechanical and robust to changes in biological environment. In this study, we used a mechanical model of the lipid bilayer to systematically investigate the influence of location, symmetry constraints, and helical forces on membrane neck constriction. Simulations from our model demonstrated that the energy barriers associated with constriction of a membrane neck are location-dependent. Importantly, if symmetry restrictions are relaxed, then the energy barrier for constriction is dramatically lowered and the membrane buckles at lower values of forcing parameters. Our simulations also show that constriction due to helical proteins further reduces the energy barrier for neck formation when compared to cylindrical proteins. These studies establish that despite different molecular mechanisms of neck formation in cells, the mechanics of constriction naturally leads to a loss of symmetry that can lower the energy barrier to constriction. 

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