A well-known problem in elasticity consists in placing two linearly elastic materials (of different shear moduli) in a given plane domain Ω, so as to maximize the torsional rigidity of the resulting rod; moreover, the proportion of these materials is prescribed. Such a problem may not have a classical solution as the optimal design may contain homogenization regions, where the two materials are...

Molecular self-assembly is an emerging subdiscipline of material science with important potential technological applications. Self-assembly is known in both molecular chemistry (for example, aggregation of molecules, molecular crystal or phase-separated polymers) and biology (for example, bilayer formation, protein folding and unfolding). Molecular self-assembly typically relies on amphiphilic ...

The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra A having a λ-cocommutative infinitesimal braiding for some regular element λ 6= 0 in the base field, then the infinitesimal braiding of A is of Hecke-type of mark...

Braided composites contain interwoven fibers that are embedded in a matrix material. Advanced measurement methods required to accurately measure and characterize braided due their composition. Micro-computed tomography (μCT) is an X-ray based method allows for the internal structure of objects be examined. High-resolution μCT geometry measured. Braid samples were measured with voxel size 1.0 μm...

The quantised braided groups were introduced recently in [1] combining Majid’s concept of braided groups [2] and the FRT formulation of quantum supergroups [3]. The generators of quantised braided groups T = T j i , i, j ∈ {1, . . . , d = dimV } satisfy the algebraic and braid relations Q12R −1 12 T1R12T2 = R −1 21 T2R21T1Q12 (1) ψ(T1 ⊗R12T2) = R12T2 ⊗R −1 12 T1R12 (2) where the numerical matri...