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Floquet Codes on Non-Trivalent Lattices

Floquet codes are a novel form of quantum error correcting codes, where the logical degrees of freedom appear in a dynamical form. The first example of such a code was constructed by Hastings and Haah on a honeycomb lattice. Specifically, they showed how to Floquetify the Kitaev honeycomb model, which when viewed as a subsystem code, encodes no logical qubits. However, by choosing a particular measurement schedule of the check operators, this model leads to dynamically encoded logical qubits. Since this initial work, several examples of Floquet codes have been constructed, mainly on trivalent lattices. Here, we report progress on understanding when such codes can be implemented on lattices of different connectivities.

Muhammad Sohaib Alam↗
NASA NTRS2009

Radial Breathing Modes in Cosmochemistry and Meteoritics

One area of continuing interest in cosmochemistry and meteoritics (C&M) is the identification of the nature of Q-phase, although some researchers in C&M are not reporting relevant portions of Raman spectral data. Q is the unidentified carrier of noble gases in carbonaceous chondrites (CCs). Being carbonaceous, the focus has been on any number of Q-candidates arising from the sp2 hybridization of carbon (C). These all derive from various forms of graphene, a monolayer of C atoms packed into a two-dimensional (2D) hexagonal honeycomb lattice that is the basic building block for graphitic materials of all other dimensions for sp2 allotropes of C. As a basic lattice, 2D graphene can be curled into fullerenes (0D), wrapped into carbon nanotubes or CNTs (1D), and stacked into graphite (3D). These take such additional forms as scroll-like carbon whiskers, carbon fibers, carbon onions, GPCs (graphite polyhedral crystals) [6], and GICs (graphite intercalation compounds). Although all of these have been observed in meteoritics, the issue is which can explain the Q-abundances. In brief, one or more of the 0D-3D sp2 hybridization forms of C is Q. For some Q-candidates, the radial breathing modes (RBMs) are the most important Raman active vibrational modes that exist, and bear a direct relevance to solving this puzzle. Typically in C&M they are ignored when present. Their importance is addressed here as smoking-gun signatures for certain Q-candidates and are very relevant to the ultimate identification of Q.

Wilson, T.L.↗
NASA NTRS2001

Lightweight Structures

Present structural concepts for hot static structures are conventional "sheet & stringer" or truss core construction. More weight-efficient concepts such as honeycomb and lattice block are being investigated, in combination with both conventional superalloys and TiAl. Development efforts for components made from TiAl sheet are centered on lower cost methods for sheet and foil production, plus alloy development for higher temperature capability. A low-cost casting technology recently developed for aluminum and steel lattice blocks has demonstrated the required higher strength and stiffness, with weight efficiency approach- ing honeycombs. The current effort is based on extending the temperature capability by developing lattice block materials made from IN-718 and Mar-M247.

Whittenberger, J. Daniel↗
NASA NTRS2003

Superalloy Lattice Block Structures

In their simplest form, lattice block panels are produced by direct casting and result in lightweight, fully triangulated truss-like configurations which provide strength and stiffness [2]. The earliest realizations of lattice block were made from A1 and steels, primarily under funding from the US Navy [3]. This work also showed that the mechanical efficiency (eg., specific stiffness) of lattice block structures approached that of honeycomb structures [2]. The lattice architectures are also less anisotropic, and the investment casting route should provide a large advantage in cost and temperature capability over honeycombs which are limited to alloys that can be processed into foils. Based on this early work, a program was initiated to determine the feasibility of extending the high temperature superalloy lattice block [3]. The objective of this effort was to provide an alternative to intermetallics and composites in achieving a lightweight high temperature structure without sacrificing the damage tolerance and moderate cost inherent in superalloys. To establish the feasibility of the superalloy lattice block concept, work was performed in conjunction with JAMCORP, Inc. Billerica, MA, to produce a number of lattice block panels from both IN71 8 and Mar-M247.

Whittenberger, J. D.↗
NASA NTRS2003

Impact Resistance of Lightweight Hybrid Structures for Gas Turbine Engine Fan Containment Applications

The ballistic impact resistance of hybrid composite sandwich structures was evaluated with the ultimate goal of developing new materials or structures for potential gas turbine engine fan containment applications. The sandwich structures investigated consisted of GLARE-5 laminates as face sheets with lightweight cellular metallic materials such as honeycomb, foam, and lattice block as a core material. The impact resistance of these hybrid sandwich structures was compared to GLARE-5 laminates and 2024-T3 Al sheet, which were tested as a function of areal weight (material thickness). The GLARE-5 laminates exhibited comparable impact properties to that of 2024-T3 Al at low areal weights, even though there were significant differences in the static tensile properties of these materials. The GLARE-5, however, did have a greater ballistic limit than straight aluminum sheet at higher areal weights. Furthermore, there is up to a 25% advantage in ballistic limit for the GLARE-5/foam sandwich structures compared to straight 2024-T3 Al. But no advantage in ballistic limit was observed between any of the hybrid sandwich structures and thicker versions of GLARE-5. Recommendations for future work are provided, based on these preliminary data.

Hebsur, Mohan G.↗
NASA NTRS1992

Extension theorems for homogenization on lattice structures

When applying homogenization techniques to problems involving lattice structures, it is necessary to extend certain functions defined on a perforated domain to a simply connected domain. This paper provides general extension operators which preserve bounds on derivatives of order l. Only the special case of honeycomb structures is considered.

Miller, Robert E.↗