Perfect 1-factorisations of circulants with small degree

A 1-factorisation of a graph G is a decomposition of G into edge-disjoint 1-factors (perfect matchings), and a perfect 1-factorisation is a 1-factorisation in which the union of any two of the 1-factors is a Hamilton cycle. We consider the problem of the existence of perfect 1-factorisations of even order circulant graphs with small degree. In particular, we characterise the 3-regular circulant graphs that admit a perfect 1-factorisation and we solve the existence problem for a large family of 4-regular circulants. Results of computer searches for perfect 1-factorisations of 4-regular circulant graphs of orders up to 30 are provided and some problems are posed

Graph Theory

This is the report on an Oberwolfach conference on graph theory, held 16-22 January 2005. There were three main components to the event: 5-minute presentations, lectures, and workshops. All participants were asked to give a 5-minute presentation of their interests on the first day, and subsequent days were divided into lectures and workshops. The latter ranged over many different topics, but the main three topics were: infinite graphs, topological methods and their use to prove theorems in graph theory, and Rota’s conjecture for matroids

On the perfect 1-factorisation problem for circulant graphs of degree 4

A 1-factorisation of a graph G is a partition of the edge set of G into 1 factors (perfect matchings); a perfect 1-factorisation of G is a 1-factorisation of G in which the union of any two of the 1-factors is a Hamilton cycle in G. It is known that for bipartite 4-regular circulant graphs, having order 2 (mod 4) is a necessary (but not sufficient) condition for the existence of a perfect 1-factorisation. The only known non-bipartite 4-regular circulant graphs that admit a perfect 1-factorisation are trivial (on 6 vertices). We prove several construction results for perfect 1-factorisations of a large class of bipartite 4-regular circulant graphs. In addition, we show that no member of an infinite family of non-bipartite 4-regular circulant graphs admits a perfect 1-factorisation. This supports the conjecture that there are no perfect 1-factorisations of any connected non-bipartite 4-regular circulant graphs of order at least 8

The effect of wing flexibility on ride comfort in formation flight

The paper addresses the issue of passenger ride comfort during formation flight. The study focuses on the vibration attenuation that occurs due to the aeroelastic effect, more particularly, on the influences these effects have on the magnitude of the fuselage accelerations. No distinction is made between the fuselage and passenger accelerations in the present work. The objective of the present study was to develop a representative aircraft model incorporating an aerodynamic model, based on the classical Vortex Lattice Method (VLM) and structural and inertial models defined by stiffness and mass matrices. The VLM code was validated for both large aspect ratio wings with low frequencies in unsteady aerodynamic conditions, as well as swept wings in steady flow, using the Warren 12 wing planform as reference. The structural model was developed using both a discretization method, as well as a continuous integration method. The results of these two approaches were carefully compared with one another as discrepancies were encountered during the analysis. The BAH jet transport wing was utilised in this study as it is widely recognised as a standard calibration case. This model was successfully implemented within a MATLAB/Simulink simulation environment. This paper presents the theoretical development of both the structural and aerodynamic models, along with the results of various test simulations. The restrained fuselage model was validated by performing a modal analysis and comparing the results with the Nastran Aeroelastic User's Guide results for a BAH wing. When the fuselage was permitted to translate vertically, a Fast Fourier Transform (FFT) was used to highlight the dominant frequencies of the system's motion and the damping ratio determined by a least squares method used to best fit the peaks of the displacement. A simple flutter analysis was performed and the results compared with those documented in the Nastran Aeroelastic User's Guide. The trailing wake vortices shed by the lead aircraft in formation flight were considered to have a solid core using the Burnham-Hallock Model. The optimal positioning of the trailing aircraft in a two-aircraft formation was discussed and all subsequent simulations run with the trailing vortex core initially located at the wing tip and 0.1 of a wingspan above the wing. The Von Karman turbulence model was used to simulate random atmospheric turbulence and the trailing vortex pair was assumed to shift in an ideal fashion within the atmospheric turbulence, resulting in fluctuating aerodynamic disturbance loads acting on the trailing aircraft. The results indicated that while the effect of turbulence on the aircraft itself was noteworthy, the motion of the trailing vortex pair in the spanwise-direction due to the turbulence, dominated the trailing aircraft's response. This was because the turbulence in the y-direction effectively altered the spanwise separation of the aircraft, varying the downwash distribution over the wing. The motion of the turbulence in the z-direction merely affected the intensity of the aerodynamic loads caused by the trailing vortices. From these results, it was concluded that an aircraft flying in formation will experience greater accelerations in turbulent conditions than a solo aircraft, due to the movement of the trailing vortices. A comparison of the motion of the airplane in response to atmospheric turbulence was compared to that documented by Fung, who made use of the Dryden turbulence model. For reasons discussed the results did not correlate exactly; however, the trends of the two sets agreed well. The individual contributions to vibrations due to shifting trailing vortices and turbulence in solo flight were analysed separately and then combined. The findings indicated that a significant difference exists between the fuselage accelerations of an aircraft with a flexible wing as opposed to a rigid wing. The results showed that the variance of the accelerations for the flexible aircraft were approximately 25% of those for the rigid aircraft. It was also found that by flying in formation the variance of the fuselage accelerations increase by approximately 18% from those of a solo aircraft flying in turbulent conditions. The predicted acceleration responses of the trailing aircraft were used as an indication of the passenger comfort levels. Thus it was concluded that while flight in formation does adversely affect the passenger ride comfort, the vibration attenuation that occurs due to the flexibility of the aircrafts wing is so significant as to minimise the discomfort levels

Proceedings, MSVSCC 2016

Proceedings of the 10th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 14, 2016 at VMASC in Suffolk, Virginia