Finding Total Unimodularity in Optimization Problems Solved by Linear Programs

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally unimodular. Still, sometimes it is possible to build an integer solution with the same cost from the fractional solution. Examples are two scheduling problems (Baptiste and Schieber, J. Sched. 6(4):395–404, 2003; Brucker and Kravchenko, J. Sched. 11(4):229–237, 2008) and the single disk prefetching/caching problem (Albers et al., J. ACM 47:969–986, 2000). We show that problems such as the three previously mentioned can be separated into two subproblems: (1) finding an optimal feasible set of slots, and (2) assigning the jobs or pages to the slots. It is straigthforward to show that the latter can be solved greedily. We are able to solve the former with a totally unimodular linear program, from which we obtain simple combinatorial algorithms with improved worst case running time.     

Quantitative characterization of nanoprecipitates in irradiated low-alloy steels: advances in the application of FEG-STEM quantitative microanalysis to real materials

The characterization of the solute-enriched features (clusters or nanoprecipitates in irradiated low-alloy steels) requires extremely high spatial and elemental resolution, previously necessitating analysis using atom probe field-ion microscopy. In this investigation, field-emission gun-scanning transmission electron microscope (FEG-STEM) quantitative energy dispersive X-ray (EDX) microanalysis (spectrum imaging) has been applied to the characterization of the irradiation-induced nanoprecipitates in a low-alloy forging steel. Refinements in the EDX data have been possible via the application of multivariate statistical analysis (MSA) to the spectrum images, resulting in significantly reduced noise in the images. Most importantly, MSA permitted the clear identification of other elements in these Ni-enriched nanoprecipitates—including Mn and Cu. The processed X-ray spectrum images also provided direct evidence of the preferential formation of these irradiation-induced features along pre-existing dislocations within the steel, as well as the formation of intragranular nanoprecipitates. This research has provided the first direct X-ray spectrum images of irradiation-induced nanoprecipitates in high Ni A508 Gr4N forging steel, and has demonstrated the significant improvements attainable though the application of MSA techniques to the spectrum images. These results independently confirmed the analyses of the Ni-enriched nanoprecipitates previously conducted by 3D-APFIM, with the performance of the FEG-STEM/EDX technique shown to be comparable to that of the 3D-APFIM technique.     

Compositional tailoring of the thermal expansion coefficient of tantalum (V) oxide

The effect of Al₂O₃ and Nb₂O₅ additions on the microstructure and thermal expansion behavior of tantalum (V) oxide has been studied. Both singly doped and co-doped compositions were examined. Compositions with 3 wt% Al₂O₃ (or greater), contained AlTaO₄ as a second phase. Complete solubility was observed for Nb₂O₅ contents in the range 1–5 wt%. It was found that doping with Al₂O₃ results in a decrease of the coefficient of thermal expansion (CTE), such that increasing amounts of Al₂O₃ (1–5 wt%) cause a successive decrease in the CTE value. In the case of Nb₂O₅ additions, the result is an increase in the CTE of the tantalum (V) oxide. However, in the range 1–5 wt% Nb₂O₅, the CTE value is relatively insensitive to the amount of Nb₂O₅ added. Due to the countervailing influences of these two additive oxides, it was demonstrated that co-doping with Al₂O₃ and Nb₂O₅ is an effective strategy for tailoring the CTE of tantalum (V) oxide.     

On debonding of graded thermal barrier coatings

Thermal barrier coatings generally consist of a metallic substrate which is the primary structural component, a metallic bond coat which serves as oxygen diffusion barrier, a very thin layer of thermally grown oxide and a ceramic top coat that provides the main thermal shielding. Homogeneous ceramic coatings as top coats appear to have certain undesirable features such as high residual and thermal stresses, generally low toughness and relatively poor bonding strength. The new concept of compositional grading of the top coat may help to overcome some of these shortcomings by eliminating the material property discontinuities. A common mode of failure in thermal barrier coatings seems to be the debonding of the top coat. In this study the related interface crack problem for a graded ceramic/metal top coat is considered. It is assumed that the thermophysical properties of the top coat continuously vary between that of the bond coat at the top coat-bond coat interface and that of the ceramic at and near the free surface. The main objective of the study is to examine the influence of the material nonhomogeneity parameters and relative dimensions on the stress intensity factors and the crack opening displacements.     

Characterization and tribological investigation of self-assembled lanthanum-based thin films on glass substrates

Rare-earth (RE) (lanthanum-based) thin films were prepared on hydroxylated glass substrates by a self-assembling process from specially formulated solution. Atomic force microscope (AFM) and X-ray photoelectron spectrometry (XPS) and scanning electron microscope (SEM) are used to characterize the thin films. The tribological properties of the as-prepared thin films sliding against a steel ball were evaluated on a friction and wear tester. The tribological experiment shows that the friction coefficient of glass substrate reduced from 0.85 to 0.13 after the formation of RE self-assembled film (SAM) on its surface. And the RE self-assembled film has longer wear life (2880 sliding pass). It is demonstrated that RE self-assembled film exhibited good wear resistant property. The superior friction reduction and wear life of RE films are attributed to good adhesion of the film to the substrate and special characteristic of the RE elements.     

The role of grain boundary energy in grain boundary complexion transitions

Recent findings about the role of the grain boundary energy in complexion transitions are reviewed. Grain boundary energy distributions are most commonly evaluated using measurements of grain boundary thermal grooves. The measurements demonstrate that when a stable high temperature complexion co-exists with a metastable low temperature complexion, the stable complexion has a lower energy. It has also been found that the changes in the grain boundary energy lead to changes in the grain boundary character distribution. Finally, recent experimental observations are consistent with the theoretical prediction that higher energy grain boundaries transform at lower temperatures than relatively lower energy grain boundaries. To better control microstructures developed through grain growth, it is necessary to learn more about the mechanism and kinetics of complexion transitions.     

Fatigue crack growth measurement in a superalloy at elevated temperature

Crack growth experiments at elevated temperature were performed in a nickel-based powder metallurgy (PM) superalloy. The crack propagation procedure was monitored by travelling microscope, high temperature extensometer and beachmarking technique. The appropriate creep crack growth relating parameter for the present alloy was discussed. The crack growth behaviours in standard compact tension specimens and side-grooved compact tension specimens were compared. Several crack length measurement techniques including beachmarking, linear correction and compliance measurement were discussed and the results were compared.     

LAMMPS framework for dynamic bonding and an application modeling DNA

We have extended the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to support directional bonds and dynamic bonding. The framework supports stochastic formation of new bonds, breakage of existing bonds, and conversion between bond types. Bond formation can be controlled to limit the maximal functionality of a bead with respect to various bond types. Concomitant with the bond dynamics, angular and dihedral interactions are dynamically introduced between newly connected triplets and quartets of beads, where the interaction type is determined from the local pattern of bead and bond types. When breaking bonds, all angular and dihedral interactions involving broken bonds are removed. The framework allows chemical reactions to be modeled, and use it to simulate a simplistic, coarse-grained DNA model. The resulting DNA dynamics illustrates the power of the present framework.Program summaryProgram title: LAMMPS Framework for Directional Dynamic BondingCatalogue identifier: AEME_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEME_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenceNo. of lines in distributed program, including test data, etc.: 2 243 491No. of bytes in distributed program, including test data, etc.: 771Distribution format: tar.gzProgramming language: C++Computer: Single and multiple core serversOperating system: Linux/Unix/WindowsHas the code been vectorized or parallelized?: Yes. The code has been parallelized by the use of MPI directives.RAM: 1 GbClassification: 16.11, 16.12Nature of problem: Simulating coarse-grain models capable of chemistry e.g. DNA hybridization dynamics.Solution method: Extending LAMMPS to handle dynamic bonding and directional bonds.Unusual features: Allows bonds to be created and broken while angular and dihedral interactions are kept consistent.Additional comments: The distribution file for this program is approximately 36 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead an html file giving details of how the program can be obtained is sent.Running time: Hours to days. The examples provided in the distribution take just seconds to run.