We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are present, the resembles densely connected ground structure. cross-sectional area of beam segments in units, modelled using Timoshenko theory, variables. All particu...

The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the first part of the paper. In the second part the theorem is applied to show that interesting combinatorial sets related to a planar graph have lattice structure: Eulerian orientations, spanning trees and Schnyder woods. For the Schnyder w...

We describe small-angle neutron scattering (SANS) studies of vortex structures in the high Tc superconductor YBazCu307 in the mixed state. The SANS technique is a unique tool for probing the crystallography of a flux line arrangement in the bulk sample that can measure the values of the characteristic lengths and the effect of defects on lattice arrangement and orientation extremely accurately....

A new approach is presented to fabricate open-cellular carbon materials with an ordered, lattice-type micro-scale architecture. The carbon micro-lattice materials were fabricated by pyrolyzing a polymer precursor template formed from an interconnected three-dimensional array of self-propagating photopolymer waveguides. Impregnating the polymer precursor template with acrylonitrile increased the...

The algebraic structure of the attractors in a dynamical system determine much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been much recent work on developing and implementing general computational algorithms for global dynamics...