We will show that, in the the geometric Lorenz flow, the set of initial states which give rise to orbits with historic behavior is residual in a trapping region.

Therapeutic dressings to enhance burn wound repair and regeneration are required. Silk fibroin (SF), a natural protein, induces cell migration and serves as a biomaterial in various dressings. SF dressings usually contain α-helices and β-sheets. The former has been confirmed to improve cell proliferation and migration, but the wound healing effect and related mechanisms of β-sheet SF remain unclear. We investigated the effects of β-sheet SF in vivo and in vitro. Alcohol-treated α-helix SF transformed into the β-sheet form, which promoted granulation formation and re-epithelialization when applied as lyophilized SF dressing (LSFD) in a rat burn model. Our in vitro results showed that β-sheet SF increased human dermal fibroblast (HDF) migration and promoted the expression of extracellular matrix (ECM) proteins (fibronectin and type III collagen), matrix metalloproteinase-12, and the cell adhesion molecule, integrin β1, in rat granulation tissue and HDFs. This confirms the role of crosstalk between integrin β1 and ECM proteins in cell migration. In summary, we demonstrated that β-sheet SF facilitates tissue regeneration by modulating cell adhesion molecules in dermal fibroblasts. LSFD could find clinical application for burn wound regeneration. Moreover, β-sheet SF could be combined with anti-inflammatory materials, growth factors, or antibiotics to develop novel dressings.

Circularly polarized luminescence (CPL) is typically achieved with a chiral luminophore. However, using a helical nanosized fused quartz cell consisting of chiral silica, we could control the wavelength and helical sense of the CPL of an achiral luminophore. Chiral silica with a helical nanostructure was prepared by calcining a mixture of polyhedral oligomeric silsesquioxane (POSS)-functionalized isotactic poly(methacrylate) (it-PMAPOSS) and a small amount of chiral dopant. The chiral silica encapsulated functional molecules, including luminophores, along the helical nanocavity, leading to induced circular dichroism (ICD) and induced circularly polarized luminescence (iCPL). Because chiral silica can act as a helical nanosized fused quartz cell, it can encapsulate not only the luminophore but also solvent molecules. By changing the solvent in the luminophore-containing nanosized fused quartz cell, the wavelength of the CPL was controlled. This method provides an effective strategy for designing novel CPL-active materials.

A strategy to obtain chiral silica using an achiral stereoregular polymer with polyhedral oligomeric silsesquioxane (POSS) side chains is described herein. The preferred helical conformation of the POSS-containing polymer could be achieved by mixing isotactic polymethacrylate-functionalized POSS (it-PMAPOSS) and a chiral dopant. The array structure of POSS molecules, which are placed along the helical conformation, is memorized even after removing the chiral dopant at high temperatures, leading to a chiral silica compound with exclusive optical activity after calcination.