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1. Stress-based topology optimization for fiber composites with improved stiffness and strength: Integrating anisotropic and isotropic materials

   https://doi.org/10.1016/j.compstruct.2023.117041  

   Kundu, Rahul Dev; Zhang, Xiaojia Shelly (September 2023, Composite Structures)
2. Sculpting the shapes of giant unilamellar vesicles using isotropic–nematic–isotropic phase cycles

   https://doi.org/10.1039/D1SM00910A  

   Jani, Purvil; Nayani, Karthik; Abbott, Nicholas L. (October 2021, Soft Matter)

   Understanding how soft matter deforms in response to mechanical interactions is central to the design of functional synthetic materials as well as elucidation of the behaviors of biological assemblies. Here we explore how cycles of thermally induced transitions between nematic (N) and isotropic (I) phases can be used to exert cyclical elastic stresses on dispersions of giant unilamellar vesicles (GUVs) and thereby evolve GUV shape and properties. The measurements were enabled by the finding that I–N–I phase transitions of the lyotropic chromonic liquid crystal disodium cromoglycate, when conducted via an intermediate columnar (M) phase, minimized transport of GUVs on phase fronts to confining surfaces. Whereas I to N phase transitions strained spherical GUVs into spindle-like shapes, with an efflux of GUV internal volume, subsequent N to I transitions generated a range of complex GUV shapes, including stomatocyte, pear- and dumbbell-like shapes that depended on the extent of strain in the N phase. The highest strained GUVs were observed to form buds (daughter vesicles) that we show, via a cycle of I–N–I–N phase transitions, are connected via a neck to the parent vesicle. Additional experiments established that changes in elasticity of the phase surrounding the GUVs and not thermal expansion of membranes were responsible for the shape transitions, and that I–N–I transformations that generate stomatocytes can be understood from the Bilayer-Coupling model of GUV shapes. Overall, these observations advance our understanding of how LC elastic stresses can be regulated to evolve the shapes of soft biological assemblies as well as provide new approaches for engineering synthetic soft matter. 

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3. Almost isotropic Kähler manifolds

   https://doi.org/10.1515/crelle-2019-0030  

   Schmidt, Benjamin; Shankar, Krishnan; Spatzier, Ralf (October 2020, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract Let M be a complete Riemannian manifold and suppose {p\in M} . For each unit vector {v\in T_{p}M} , the Jacobi operator , {\mathcal{J}_{v}:v^{\perp}\rightarrow v^{\perp}} is the symmetric endomorphism, {\mathcal{J}_{v}(w)=R(w,v)v} . Then p is an isotropic point if there exists a constant {\kappa_{p}\in{\mathbb{R}}} such that {\mathcal{J}_{v}=\kappa_{p}\operatorname{Id}_{v^{\perp}}} for each unit vector {v\in T_{p}M} . If all points are isotropic, then M is said to be isotropic; it is a classical result of Schur that isotropic manifolds of dimension at least 3 have constant sectional curvatures. In this paper we consider almost isotropic manifolds , i.e. manifolds having the property that for each {p\in M} , there exists a constant {\kappa_{p}\in\mathbb{R}} such that the Jacobi operators {\mathcal{J}_{v}} satisfy {\operatorname{rank}({\mathcal{J}_{v}-\kappa_{p}\operatorname{Id}_{v^{\perp}}}% )\leq 1} for each unit vector {v\in T_{p}M} . Our main theorem classifies the almost isotropic simply connected Kähler manifolds, proving that those of dimension {d=2n\geqslant 4} are either isometric to complex projective space or complex hyperbolic space or are totally geodesically foliated by leaves isometric to {{\mathbb{C}}^{n-1}} . 

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4. Assembly of particle strings via isotropic potentials

   https://doi.org/10.1063/1.5088604  

   Banerjee, D.; Lindquist, B. A.; Jadrich, R. B.; Truskett, T. M. (March 2019, The Journal of Chemical Physics)
5. Elastocaloric Response of Isotropic Liquid Crystalline Elastomers

   https://doi.org/10.1002/smll.202400786  

   Herman, Jeremy A; Hoang, Jonathan D; White, Timothy J (August 2024, Small)

   Liquid crystalline elastomers (LCEs) are soft materials that associate order and deformation. Upon deformation, mechanically induced changes order affect entropy and can produce a caloric output (elastocaloric). Elastocaloric effects in materials continue to be considered for functional use as solid state refrigerants. Prior elastocaloric investigations of LCEs and related materials have measured ≈2 °C temperature changes upon deformation (100% strain). Here, the elastocaloric response of LCEs is explored that are prepared with a subambient nematic to isotropic transition temperature. These materials are referred as “isotropic” liquid crystalline elastomers. The LCEs are prepared by a two‐step thiol‐Michael/thiol‐ene reaction. This polymer network chemistry enhances elastic recovery and reduces hysteresis compared to acrylate‐based chemistries. The LCEs exhibit appreciable elastocaloric temperature changes upon deformation and recovery (> ± 3 °C, total ΔTof 6 °C) to deformation driven by minimal force (<< 1 MPa). Notably, the strong association of deformation and order and the resulting temperature change attained at low force achieves a responsivity of 14 °C MPa⁻¹which is seven times greater than natural rubber. 

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