Optimal routing of military convoys through a road network

To wage a successful campaign, military units and materiel must be in position by the designated time. This thesis models the problem of moving military units and materiel in convoys through a road network as mathematical programming models. In particular, two models, linear and integer, are investigates. both models belong to the class of multicommodity, dynamic transshipment network problems. Based on prototypic GAMS implementations, they provide essentially the same answer. However, the linear model is easier to construct, takes less time to solve and allows for more flexible convoy routing.http://archive.org/details/optimalroutingof00leedMajor, Republic of Korea ArmyApproved for public release; distribution is unlimited

Scaling of cluster heterogeneity in percolation transitions

We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an occupation probability $p$ increases, the cluster size distribution evolves from a monodisperse distribution to a polydisperse one in the subcritical phase, and back to a monodisperse one in the supercritical phase. We show analytically that $H$ diverges algebraically approaching the percolation critical point $p_c$ as $H\sim |p-p_c|^{-1/\sigma}$ with the critical exponent $\sigma$ associated with the characteristic cluster size. Interestingly, its finite-size-scaling behavior is governed by a new exponent $\nu_H = (1+d_f/d)\nu$ where $d_f$ is the fractal dimension of the critical percolating cluster and $\nu$ is the correlation length exponent. The corresponding scaling variable defines a singular path to the critical point. All results are confirmed by numerical simulations.Comment: 4 pages, 4 figure

Observation of chiral quantum-Hall edge states in graphene

In this study, we determined the chiral direction of the quantum-Hall (QH) edge states in graphene by adopting simple two-terminal conductance measurements while grounding different edge positions of the sample. The edge state with a smaller filling factor is found to more strongly interact with the electric contacts. This simple method can be conveniently used to investigate the chirality of the QH edge state with zero filling factor in graphene, which is important to understand the symmetry breaking sequence in high magnetic fields ($\gtrsim$25 T).Comment: 3 pages, 3 figures. Appeared in AP

Dependence of quantum-Hall conductance on the edge-state equilibration position in a bipolar graphene sheet

By using four-terminal configurations, we investigated the dependence of longitudinal and diagonal resistances of a graphene p-n interface on the quantum-Hall edge-state equilibration position. The resistance of a p-n device in our four-terminal scheme is asymmetric with respect to the zero point where the filling factor ($\nu$) of the entire graphene vanishes. This resistance asymmetry is caused by the chiral-direction-dependent change of the equilibration position and leads to a deeper insight into the equilibration process of the quantum-Hall edge states in a bipolar graphene system.Comment: 5 pages, 4 figures, will be published in PR

Thermoelectric Transport of Massive Dirac Fermions in Bilayer Graphene

Thermoelectric power (TEP) is measured in bilayer graphene for various temperatures and charge-carrier densities. At low temperatures, measured TEP well follows the semiclassical Mott formula with a hyperbolic dispersion relation. TEP for a high carrier density shows a linear temperature dependence, which demonstrates a weak electron-phonon interaction in the bilayer graphene. For a low carrier density, a deviation from the Mott relation is observed at high temperatures and is attributed to the low Fermi temperature in the bilayer graphene. Oscillating TEP and the Nernst effect for varying carrier density, observed in a high magnetic field, are qualitatively explained by the two dimensionality of the system.Comment: published versio

Inelastic scattering in a monolayer graphene sheet; a weak-localization study

Charge carriers in a graphene sheet, a single layer of graphite, exhibit much distinctive characteristics to those in other two-dimensional electronic systems because of their chiral nature. In this report, we focus on the observation of weak localization in a graphene sheet exfoliated from a piece of natural graphite and nano-patterned into a Hall-bar geometry. Much stronger chiral-symmetry-breaking elastic intervalley scattering in our graphene sheet restores the conventional weak localization. The resulting carrier-density and temperature dependence of the phase coherence length reveal that the electron-electron interaction including a direct Coulomb interaction is the main inelastic scattering factor while electron-hole puddles enhance the inelastic scattering near the Dirac point.Comment: 12 pages, 3 figures, submitted to PR