Minimum degrees for powers of paths and cycles

We study minimum degree conditions under which a graph $G$ contains $k^{th}$ power of paths and cycles of arbitrary specified lengths. We determine precise thresholds, assuming that the order of G is large. This extends a result of Allen, B\"ottcher and Hladk\'y concerning the containment of squares of paths and squares of cycles of arbitrary specified lengths and settles a conjecture of theirs in the affirmative.Comment: 69 pages, 3 figures. arXiv admin note: text overlap with arXiv:0906.3299 by other author

The effect of inclination and stand-off on the dynamic response of beams impacted by slugs of a granular material

The dynamic response of end-clamped sandwich and monolithic beams to impact by highvelocity tungsten carbide (WC) particle columns (slugs) has been measured with the aim of developing an understanding of the interaction of ejecta from a shallow-buried explosion with structures. The monolithic beams were made from stainless steel, while the sandwich beams of equal areal mass comprised stainless steel face sheets and an aluminium honeycomb core. High-speed imaging was used to measure the transient transverse deflection of the beams, to record the dynamic modes of deformation, and to observe the flow of the WC particles upon impact. The experiments show that sandwich beams deflect less than the monolithic beams both in normal and inclined impact situations. Moreover, the deflections of all beams in the inclined orientation were less than their respective deflections in the normal orientation at the same slug velocity. Intriguingly, the ratio of the deflection of the sandwich to monolithic beams remains approximately constant with increasing slug velocity for inclined impact but increases for normal impact; i.e. inclined sandwich beams retain their advantage over monolithic beams with increasing slug velocity. Dynamic force measurements reveal that (i) the momentum transferred from the impacting slug to both monolithic and sandwich beams is the same, and (ii) the interaction between the impacting particles and the dynamic deformation of the inclined monolithic and sandwich beams results in a momentum transfer into these beams that is equal to or greater than the momentum of the slug. These experimental findings demonstrate that contrary to intuition and widespread belief, the performance enhancement obtained from employing beam inclination is not due to a reduction in transferred momentum. Finally, we show that increasing the stand-off distance decreases beam deflections. This is because the slugs lengthen as they traverse towards their target and thus the duration of loading is extended with increasing stand-off. However, combining increased stand-off with sandwich construction does not yield the synergistic benefits of sandwich construction combined with beam inclination.The work was supported by the Office of Naval Research Grant N00014-09-1-0573 (Program manager, Dr. David Shifler) and the Defense Advanced Projects Agency under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser).This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0020768314004466

Momentum transfer during the impact of granular matter with inclined sliding surfaces

© 2017 Elsevier Ltd Increasing the inclination of a rigid surface that is impacted by a collimated granular flow reduces the fraction of granular matter momentum transferred to the surface. Recent studies have shown that the momentum reduction depends upon a frictional interaction between the granular flow and the impacted surface. High coefficient of friction surfaces suffer significantly more momentum transfer than predicted by resolution of the incident momentum onto the inclined plane. This discovery has raised the possibility that inclined surfaces with very low friction coefficients might reduce the impulsive transferred by the impact of high velocity granular matter. Here the use of a lubricated sliding plate is investigated as a means for reducing interfacial friction and impulse transfer to an inclined surface. The study uses a combination of experimental testing and particle-based simulations to investigate impulse transfer to rigid aluminum surfaces inclined either perpendicular or at 53° to synthetic sand that was impulsively accelerated to a velocity of 350–500 m/s. The study shows that impact of this sand with lubricated plates attached to an inclined surface rapidly accelerates them to a velocity of about 55–70 m/s, and reduces the impulse transferred to the inclined surface below. The reduction of impulse by this approach is comparable to that achieved by changing the inclination of the surface.This research was funded by the Defense Advanced Research Projects Agency (DARPA) under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser)

Deep penetration of ultra-high molecular weight polyethylene composites by a sharp-tipped punch

The penetration of unidirectional (UD) and [0#/90#] cross-ply ultra-high molecular weight polyethylene fibre composites by sharp-tipped cylindrical punches has been investigated. While the measured penetration pressure for both composite types increased with decreasing punch diameter, the pressure was significantly higher for the cross-ply composites and increased with decreasing ply thickness. A combination of optical microscopy and X-ray tomography revealed that in both composites, the sharp-tipped punch penetrated without fibre fracture by the formation of mode-I cracks along the fibre directions, followed by the wedging open of the crack by the advancing punch. In the cross-ply composites, delamination between adjacent 0# and 90# plies also occurred to accommodate the incompatible deformation between plies containing orthogonal mode-I cracks. Micromechanical models for the steadystate penetration pressure were developed for both composites. To account for material anisotropy as well as the large shear strains and fibre rotations, the deformation of the composites was modelled via a pressure-dependent crystal plasticity framework. Intra and inter-ply fracture were accounted for via mode-I and delamination toughnesses respectively. These models account for the competition between deformation and fracture of the plies and accurately predict the measured steady-state penetration pressures over the wide range of punch diameters and ply thicknesses investigated here. Design maps for the penetration resistance of cross-ply composites were constructed using these models and subsequently used to infer composite designs that maximise the penetration resistance for a user prescribed value of fibre strength.DARP

Job Demands, Job Resources and Work Stress: A Study Among Customs Officers In Malaysia

The main purpose of this research is to examine the relationships of job demands, job resources and work stress among customs officers in Malaysia. The survey questionnaire was designed to elicit responses from the participants. A total of 800 questionnaires were distributed to the employees of the Royal Malaysian Customs Department. There are 215 usable questionnaires were returned, yielding a response rate of 26.9%. The collected data were analyzed using the Statistical Package for Social Science (SPSS) version 25. The results indicated that job demands were positively related to work stress. On the other hand, job resources were found negatively related to work stress. The findings showed that Customs Officers were suffered from work stress due to job demands yet the job resources reduced their work stress. Thus, the Royal Malaysian Customs Department must put a great emphasis on the significant roles played by job demands and job resources to reduce employee’s stress levels in the organization

Coupled discrete/continuum simulations of the impact of granular slugs with clamped beams: stand-off effects

Coupled discrete particle/continuum simulations of the normal (zero obliquity) impact of granular slugs against the centre of deformable, end-clamped beams are reported. The simulations analyse the experiments of Uth et al. (2015) enabling a detailed interpretation of their observations of temporal evolution of granular slug and a strong stand-off distance dependence of the structural response. The high velocity granular slugs were generated by the pushing action of a piston and develop a spatial velocity gradient due to elastic energy stored during the loading phase by the piston. The velocity gradient within the “stretching” slug is a strong function of the inter-particle contact stiffness and the time the piston takes to ramp up to its final velocity. Other inter-particle contact properties such as damping and friction are shown to have negligible effect on the evolution of the granular slug. The velocity gradients result in a slug density that decreases with increasing stand-off distance, and therefore the pressure imposed by the slug on the beams is reduced with increasing stand-off. This results in the stand-off dependence of the beam's deflection observed by Uth et al. (2015). The coupled simulations capture both the permanent deflections of the beams and their dynamic deformation modes with a high degree of fidelity. These simulations shed new light on the stand-off effect observed during the loading of structures by shallow-buried explosions

Embedding problems in graphs and hypergraphs

In this thesis, we explore several mathematical questions about substructures in graphs and hypergraphs, focusing on algorithmic methods and notions of regularity for graphs and hypergraphs. We investigate conditions for a graph to contain powers of paths and cycles of arbitrary specified linear lengths. Using the well-established graph regularity method, we determine precise minimum degree thresholds for sufficiently large graphs and show that the extremal behaviour is governed by a family of explicitly given extremal graphs. This extends an analogous result of Allen, Böttcher and Hladký for squares of paths and cycles of arbitrary specified linear lengths and confirms a conjecture of theirs. Given positive integers k and j with j < k, we study the length of the longest j-tight path in the binomial random k-uniform hypergraph Hk(n, p). We show that this length undergoes a phase transition from logarithmic to linear and determine the critical threshold for this phase transition. We also prove upper and lower bounds on the length in the subcritical and supercritical ranges. In particular, for the supercritical case we introduce the Pathfinder algorithm, a depth-first search algorithm which discovers j-tight paths in a k-uniform hypergraph. We prove that, in the supercritical case, with high probability this algorithm finds a long j-tight path. Finally, we investigate the embedding of bounded degree hypergraphs into large sparse hypergraphs. The blow-up lemma is a powerful tool for embedding bounded degree spanning subgraphs with wide-ranging applications in extremal graph theory. We prove a sparse hypergraph analogue of the blow-up lemma, showing that large sparse partite complexes with sufficiently regular small subcomplex counts and no atypical vertices behave as if they were complete for the purpose of embedding complexes with bounded degree and bounded partite structure