Reaching Approximate Byzantine Consensus with Multi-hop Communication

We address the problem of reaching consensus in the presence of Byzantine faults. In particular, we are interested in investigating the impact of messages relay on the network connectivity for a correct iterative approximate Byzantine consensus algorithm to exist. The network is modeled by a simple directed graph. We assume a node can send messages to another node that is up to $l$ hops away via forwarding by the intermediate nodes on the routes, where $l\in \mathbb{N}$ is a natural number. We characterize the necessary and sufficient topological conditions on the network structure. The tight conditions we found are consistent with the tight conditions identified for $l=1$, where only local communication is allowed, and are strictly weaker for $l>1$. Let $l^*$ denote the length of a longest path in the given network. For $l\ge l^*$ and undirected graphs, our conditions hold if and only if $n\ge 3f+1$ and the node-connectivity of the given graph is at least $2f+1$ , where $n$ is the total number of nodes and $f$ is the maximal number of Byzantine nodes; and for $l\ge l^*$ and directed graphs, our conditions is equivalent to the tight condition found for exact Byzantine consensus. Our sufficiency is shown by constructing a correct algorithm, wherein the trim function is constructed based on investigating a newly introduced minimal messages cover property. The trim function proposed also works over multi-graphs.Comment: 24 pages, 1 figure. arXiv admin note: text overlap with arXiv:1203.188

Production of large-particle-size monodisperse latexes

The research program achieved two objectives: (1) it has refined and extended the experimental techniques for preparing monodisperse latexes in quantity on the ground up to a particle diameter of 10 microns; and (2) it has demonstrated that a microgravity environment can be used to grow monodisperse latexes to larger sizes, where the limitations in size have yet to be defined. The experimental development of the monodisperse latex reactor (MLR) and the seeded emulsion polymerizations carried out in the laboratory prototype of the flight hardware, as a function of the operational parameters is discussed. The emphasis is directed towards the measurement, interpretation, and modeling of the kinetics of seeded emulsion polymerization and successive seeded emulsion polymerization. The recipe development of seeded emulsion polymerization as a function of particle size is discussed. The equilibrium swelling of latex particles with monomers was investigated both theoretically and experimentally. Extensive studies are reported on both the type and concentration of initiators, surfactants, and inhibitors, which eventually led to the development of the flight recipes. The experimental results of the flight experiments are discussed, as well as the experimental development of inhibition of seeded emulsion polymerization in terms of time of inhibition and the effect of inhibitors on the kinetics of polymerization

Laser pulse annealing of ion-implanted GaAs

GaAs single-crystals wafers are implanted at room temperature with 400-keV Te + ions to a dose of 1×10^15 cm^–2 to form an amorphous surface layer. The recrystallization of this layer is investigated by backscattering spectrometry and transmission electron microscopy after transient annealing by Q-switched ruby laser irradiation. An energy density threshold of about 1.0 J/cm^2 exists above which the layer regrows epitaxially. Below the threshold the layer is polycrystalline; the grain size increases as the energy density approaches threshold. The results are analogous to those reported for the elemental semiconductors, Si and Ge. The threshold value observed is in good agreement with that predicted by the simple model successfully applied previously to Si and Ge

Primary breakup in gas/liquid mixing layers for turbulent liquids

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77169/1/AIAA-1992-462-385.pd

Effects of ambient gas density on the structure of pressure-atomizedsprays

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77110/1/AIAA-1991-690-582.pd

Dispersed-phase structure of pressure-atomized sprays at various gasdensities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76056/1/AIAA-1992-230-405.pd