Distinct difference configurations: multihop paths and key predistribution in sensor networks

A distinct difference configuration is a set of points in Z2 with the property that the vectors (difference vectors) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the k-hop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of k or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the k-hop coverage of a distinct difference configuration with m points, and exploit a connection with Bh sequences to construct configurations with maximal k-hop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application

Two-dimensional patterns with distinct differences; constructions, bounds, and maximal anticodes

A two-dimensional (2-D) grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many applications such as radar, sonar, physical alignment, and time-position synchronization. Rather than restricting dots to lie in a square or rectangle, as previously studied, we restrict the maximum distance between dots of the configuration; the motivation for this is a new application of such configurations to key distribution in wireless sensor networks. We consider configurations in the hexagonal grid as well as in the traditional square grid, with distances measured both in the Euclidean metric, and in the Manhattan or hexagonal metrics. We note that these configurations are confined inside maximal anticodes in the corresponding grid. We classify maximal anticodes for each diameter in each grid. We present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes. Our bounds settle (in the negative) a question of Golomb and Taylor on the existence of honeycomb arrays of arbitrarily large size. We present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various 2-D shapes (such as anticodes) by considering periodic configurations with distinct differences in the square grid

Shadowing Effects on Particle and Transverse Energy Production

The effect of shadowing on the early state of ultrarelativistic heavy ion collisions and transverse energy production is discussed. Results are presented for RHIC Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV and LHC Pb+Pb collisions at $\sqrt{s_{NN}} = 5.5$ TeV.Comment: 4 pgs, 2 figures, presented at Quark Matter '9

Nucleons Properties at Finite Lattice Spacing in Chiral Perturbation Theory

Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.Comment: 16 pages LaTe

BcB_c Physics at Hadron Colliders

In this paper we summarize the results of the theory working group dedicated to the analysis of $B_c$ production at hadron colliders.Comment: 7 pages, LaTe

Staggered flux and stripes in doped antiferromagnets

We have numerically investigated whether or not a mean-field theory of spin textures generate fictitious flux in the doped two dimensional $t-J$-model. First we consider the properties of uniform systems and then we extend the investigation to include models of striped phases where a fictitious flux is generated in the domain wall providing a possible source for lowering the kinetic energy of the holes. We have compared the energetics of uniform systems with stripes directed along the (10)- and (11)-directions of the lattice, finding that phase-separation generically turns out to be energetically favorable. In addition to the numerical calculations, we present topological arguments relating flux and staggered flux to geometric properties of the spin texture. The calculation is based on a projection of the electron operators of the $t-J$ model into a spin texture with spinless fermions.Comment: RevTex, 19 pages including 20 figure

Strongly Interacting W's and Z's and the Existence of a Heavy Fourth Generation of Fermions

By employing the dictum that axiomatic principles are devoid of predictive power, we find that the elastic unitarity constraint, applied to strong W$_L$W$_L$ scattering, does not alter the assumed spectrum of intermediate states. We consider intermediate states involving a heavy Higgs and heavy fermions of a hypothetical fourth generation doublet. In contrast to recent studies, we find no p-wave resonance, and therefore no violation of the S parameter upper bound. We conclude that the elastic unitarity constraint sheds no light on the existence of a heavy fourth generation.Comment: 8 pages including 4 uuencoded, tarred, and compressed postscript figures, CPP-93-0

Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic $2\times 12$ ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of $\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic $(\lambda=1)$ spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.Comment: 22 pages. 9 figure

Structural modelling and testing of failed high energy pipe runs: 2D and 3D pipe whip

Copyright @ 2011 ElsevierThe sudden rupture of a high energy piping system is a safety-related issue and has been the subject of extensive study and discussed in several industrial reports (e.g. [2], [3] and [4]). The dynamic plastic response of the deforming pipe segment under the blow-down force of the escaping liquid is termed pipe whip. Because of the potential damage that such an event could cause, various geometric and kinematic features of this phenomenon have been modelled from the point of view of dynamic structural plasticity. After a comprehensive summary of the behaviour of in-plane deformation of pipe runs [9] and [10] that deform in 2D in a plane, the more complicated case of 3D out-of-plane deformation is discussed. Both experimental studies and modelling using analytical and FE methods have been carried out and they show that, for a good estimate of the “hazard zone” when unconstrained pipe whip motion could occur, a large displacement analysis is essential. The classical, rigid plastic, small deflection analysis (e.g. see [2] and [8]), is valid for estimating the initial failure mechanisms, however it is insufficient for describing the details and consequences of large deflection behaviour

Suppression of static stripe formation by next-neighbor hopping

We show from real-space Hartree-Fock calculations within the extended Hubbard model that next-nearest neighbor (t') hopping processes act to suppress the formation of static charge stripes. This result is confirmed by investigating the evolution of charge-inhomogeneous corral and stripe phases with increasing t' of both signs. We propose that large t' values in YBCO prevent static stripe formation, while anomalously small t' in LSCO provides an additional reason for the appearance of static stripes only in these systems.Comment: 4 pages, 5 figure