Dissolution-driven propulsion of floating solids

We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale sugar and salt slabs attached to a buoy are observed to move rapidly in water with speeds up to 5 mm/s determined by the inclination angle and orientation of the dissolving surfaces. While symmetric boats drift slowly, asymmetric boats are observed to accelerate rapidly along a line before reaching a terminal velocity when their drag matches the thrust generated by dissolution. By visualizing the flow around the body, we show that the boat velocity is always directed opposite to the horizontal component of the density current. We derive the thrust acting on the body from its measured kinematics and show that the propulsion mechanism is consistent with the unbalanced momentum generated by the attached density current. We obtain an analytical formula for the body speed depending on geometry and material properties and show that it captures the observed trends reasonably. Our analysis shows that the gravity current sets the scale of the body speed consistent with our observations, and we estimate that speeds can grow slowly as the cube root of the length of the inclined dissolving surface. The dynamics of dissolving solids demonstrated here applies equally well to solids undergoing phase change and may enhance the drift of melting icebergs, besides unraveling a primal strategy by which to achieve locomotion in active matter. © 2023 the Author(s)

College Algebra (University of North Georgia)

This Grants Collection Open Textbook for College Algebra was created under a Round Two ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/mathematics-collections/1010/thumbnail.jp

Intermediate Algebra

This Grants Collection for Intermediate Algebra was created under a Round Two ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/mathematics-collections/1012/thumbnail.jp

Support for College Algebra

This Grants Collection for Support for College Algebra was created under a Round Two ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/mathematics-collections/1013/thumbnail.jp

Forced three-wave interactions of capillary-gravity surface waves

Editors' suggestionInternational audienceThree-wave resonant interactions constitute an essential nonlinear mechanism coupling capillary surface waves. In a previous work [Haudin et al. Phys. Rev. E 93, 043110 (2016)], we characterized experimentally the generation by this mechanism of a daughter wave, whose amplitude saturates due to the viscous dissipation. Here, we show experimentally the generation of a daughter wave verifying the resonant conditions, but not the dispersion relation. By modeling the response of the free surface at the lowest nonlinear order, we explain this observation as a forced interaction. The bandwidth of the linear transfer function of the free surface is indeed increased by the significant viscous dissipation. The observation of free surface excitations not following the linear dispersion relation then becomes possible. This forced three-wave interaction mechanism could have important consequences for wave turbulence in experimental or natural systems with nonnegligible dissipation