The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus

We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\mathbb{R}^3$ with a fixed periodic lattice.Comment: 31 pages, 12 figure

Binary mixture of hard disks as a model glass former: Caging and uncaging

I have proposed a measure for the cage effect in glass forming systems. A binary mixture of hard disks is numerically studied as a model glass former. A network is constructed on the basis of the colliding pairs of disks. A rigidity matrix is formed from the isostatic (rigid) sub--network, corresponding to a cage. The determinant of the matrix changes its sign when an uncaging event occurs. Time evolution of the number of the uncaging events is determined numerically. I have found that there is a gap in the uncaging timescales between the cages involving different numbers of disks. Caging of one disk by two neighboring disks sustains for a longer time as compared with other cages involving more than one disk. This gap causes two--step relaxation of this system

Analysis of the Public Works Service Request Process For Naval Facilities Engineering Command Northwest

EMBA Project ReportEXECUTIVE SUMMARY: The goal of this project is to analyze the service request portion of the Public Works Business Line (PWBL) processes for Naval Facilities Engineering Command (NAVFAC) Northwest. All four PWBL Product Lines are included in the analysis. These Product Lines are Facility Management and Sustainment (FM&S), Facility Service Contract Management and Facility Services (FMFS), Base Support Vehicles and Equipment (BSVE), and Utilities and Energy Management (UEM). The perceived problem is that there are instances of confusion and inaccuracies regarding funding responsibilities and service levels resulting from prior years of organizational changes and functional transfers. The research examines the process used to contact NAVFAC to request service, the process NAVFAC uses to validate that the requested service is funded and authorized, and applicable documents, agreements, and information used by the participants. By conducting interviews with fifty process participants, sufficient information is gathered to map the current service request process. Process maps are provided for each product line. The maps show the decision points involved in the interaction between the customer and NAVFAC field staff in the request process. The interview results confirm that the perceived problems do exist in some areas and product lines. Interviewed personnel credit NAVFAC for improvements already accomplished in many areas. Remaining problems common to multiple product lines and cited most often include limited resources, limited access to NAVFAC information, unclear service level and funding source information, and insufficient sharing of long range planning information between customers and NAVFAC. In addition, the use of authorized customer representatives and regular customer meetings work well when used and could be leveraged in other areas. After conducting root cause analysis, recommendations are provided that address the consequences of the problems and align with NAVFAC strategic goals. These include communication improvements to increase accessibility of information, documentation improvements to reduce confusion, and training suggestions to improve understanding and consistency. The recommendations are charted with benefits and difficulty of implementation to assist NAVFAC in deciding which to consider implementing first (i.e., those with the most benefit for the least initial investment). A tool is included to allow the client to adjust the value weighting of the benefits and implementation difficulty based on their own preferences. Using equal weighting the recommendations to consider first are: a) the communication recommendations including an accessible web site, holding a customer symposium, and publications, b) the documentation recommendation of posting the process maps, and c) the training recommendations to hold internal briefings for NAVFAC personnel and acquisition briefings for customers. Implementation of even some of the recommendations provided in this study will achieve many benefits in operational effectiveness for both NAVFAC and its supported Commands.http://archive.org/details/analysisofpublic10945707

Multi-triangulations as complexes of star polygons

Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of looking at $k$-triangulations, namely as complexes of star polygons. With this tool we give new, direct, proofs of the fundamental properties of $k$-triangulations, as well as some new results. This interpretation also opens-up new avenues of research, that we briefly explore in the last section.Comment: 40 pages, 24 figures; added references, update Section

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

Multilayer Corrosion of Aluminum Activated by Lead

Segregation of Pb as a nanofilm between the thermal oxide and the metal substrate as a result of high temperature heat-treatment is known to activate aluminum alloys anodically in chloride solution. The relationship between the oxidation peaks in the polarization curve and corrosion morphology was investigated by the use of a video technique during electrochemical polarization. A model binary Al–Pb alloy containing 20 ppm Pb, which was annealed at 600°C, showed two oxidation peaks at −0.95 and −0.88 V_SCE. The video measurements revealed superficial etching of the surface by selective oxidation of the aluminum metal twice, followed each time by repassivation, as the two oxidation peaks were resolved during anodic potentiodynamic sweep. Ex situ scanning and transmission electron microscopy of the corroded specimens indicated that the first layer of etching followed the Pb film and undermined the thermal oxide, which remained attached to the metal surface at discrete locations, thereby forming a crevice. The second layer of attack was caused by crevice corrosion of the aluminum substrate in the crevice formed by the preceding oxidation process, which resulted in the removal of the attached thermal oxide film. The exposed aluminum substrate started to pit as the pitting potential was finally exceeded

Algorithms for 3D rigidity analysis and a first order percolation transition

A fast computer algorithm, the pebble game, has been used successfully to study rigidity percolation on 2D elastic networks, as well as on a special class of 3D networks, the bond-bending networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on BCC and FCC lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first order rigidity percolation transition, which is in contrast to the second order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed for Bethe lattices and networks with ``chemical order'', this is the first time it has been seen for a regular randomly diluted network. In the case of site dilution, the transition is also first order for BCC, but results for FCC suggest a second order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent non-universality, make this phase transition highly unusual.Comment: 28 pages, 19 figure