An exploration of two infinite families of snarks

Thesis (M.S.) University of Alaska Fairbanks, 2019In this paper, we generalize a single example of a snark that admits a drawing with even rotational symmetry into two infinite families using a voltage graph construction techniques derived from cyclic Pseudo-Loupekine snarks. We expose an enforced chirality in coloring the underlying 5-pole that generated the known example, and use this fact to show that the infinite families are in fact snarks. We explore the construction of these families in terms of the blowup construction. We show that a graph in either family with rotational symmetry of order m has automorphism group of order m2m⁺¹. The oddness of graphs in both families is determined exactly, and shown to increase linearly with the order of rotational symmetry.Chapter 1: Introduction -- 1.1 General Graph Theory -- Chapter 2: Introduction to Snarks -- 2.1 History -- 2.2 Motivation -- 2.3 Loupekine Snarks and k-poles -- 2.4 Conditions on Triviality -- Chapter 3: The Construction of Two Families of Snarks -- 3.1 Voltage Graphs and Lifts -- 3.2 The Family of Snarks, Fm -- 3.3 A Second Family of Snarks, Rm -- Chapter 4: Results -- 4.1 Proof that the graphs Fm and Rm are Snarks -- 4.2 Interpreting Fm and Rm as Blowup Graphs -- 4.3 Automorphism Group -- 4.4 Oddness -- Chapter 5: Conclusions and Open Questions -- References

An environment for object-oriented real-time system design

A concise object-oriented method for the development of real-time systems has been composed. Hardware components are modelled by (software) base objects; base objects are controlled by a hierarchy of coordinator objects, expressed in an organizational diagram. The behaviour of objects is specified by state transition diagrams. This approach considerably promotes requirements analysis and communication with the customer. A CASE tool has been constructed with diagram editors for graphical specifications of real-time systems. The tool can generate executable code for PLCs from these graphical specifications; reuse of previous results is supported by the repository function of the tool. Experiences attained in practice with method and tool show that time spent in system testing and installation is reduced considerabl

Estimating Abundance from Counts in Large Data Sets of Irregularly-Spaced Plots using Spatial Basis Functions

Monitoring plant and animal populations is an important goal for both academic research and management of natural resources. Successful management of populations often depends on obtaining estimates of their mean or total over a region. The basic problem considered in this paper is the estimation of a total from a sample of plots containing count data, but the plot placements are spatially irregular and non randomized. Our application had counts from thousands of irregularly-spaced aerial photo images. We used change-of-support methods to model counts in images as a realization of an inhomogeneous Poisson process that used spatial basis functions to model the spatial intensity surface. The method was very fast and took only a few seconds for thousands of images. The fitted intensity surface was integrated to provide an estimate from all unsampled areas, which is added to the observed counts. The proposed method also provides a finite area correction factor to variance estimation. The intensity surface from an inhomogeneous Poisson process tends to be too smooth for locally clustered points, typical of animal distributions, so we introduce several new overdispersion estimators due to poor performance of the classic one. We used simulated data to examine estimation bias and to investigate several variance estimators with overdispersion. A real example is given of harbor seal counts from aerial surveys in an Alaskan glacial fjord.Comment: 37 pages, 7 figures, 4 tables, keywords: sampling, change-of-support, spatial point processes, intensity function, random effects, Poisson process, overdispersio

Fluid-particle interaction force for polydisperse systems from lattice boltzmann simulations

Gas-solid fluidized beds are almost always polydisperse in industrial\ud application. However, to describe the fluid-particle interaction\ud force in models for large-scale gas-solid flow, relations\ud are used which have been derived for monodisperse system, for\ud which ad-hoc modifications are made to account for polydispersity.\ud Recently it was shown, on the basis of detailed lattice\ud Boltzmann simulations, that for bidisperse systems these\ud modifications predict a drag force which can be factors different\ud from the true drag force. In this work fluid-particle interaction\ud forces for polydisperse system are studied by means of\ud lattice Boltzmann simulation, using a grid that is typically an\ud order of magnitude smaller than the sphere diameter. Two different\ud lognormal size distributions are considered for this study.\ud The systems consist of polydisperse random arrays of spheres\ud in the diameter range of 8-24 grid spacing and 8-40 grid spacing,\ud a solid volume fraction of 0.5 and 0.3 and Reynolds number\ud 0.1 to 500. The data confirms the observations made for bidisperse\ud systems, namely that an extra correction factor for the\ud drag force is required to adequately capture the effect of polydispersity.\ud It was found that the correction factor derived by van\ud der Hoef et al (J. Fluid Mech. 528 (2005) 233) on the basis of\ud bidisperse simulation data, applies also to general polydisperse\ud system

The influence of the (2 × 1) reconstruction of the Si(1 0 0) surface on the Si---L2,3 VV Auger lineshape

The extreme surface sensitiveness of the Si---L2,3 VV Auger process and its ability to probe the atomic electron distribution in the direct neighbourhood of the L2,3-core-hold makes this electron spectroscopic technique a candidate for investigations of the local changes in the electron distribution due to surface reconstruction. In this paper we show, explicitly, the influence of the (2 × 1) reconstruction of the Si(1 0 0) surface on the Si---L2,3 VV Auger lineshape. Furthermore, the calculated Auger lineshape will be compared with an experimentally obtained line profile

Line tension and wettability of nanodrops on curved surfaces

In this paper we study the formation of nanodrops on curved surfaces (both convex and concave) by means of molecular dynamics simulations, where the particles interact via a Lennard-Jones potential. We find that the contact angle is not affected by the curvature of the substrate, in agreement with previous experimental findings. This means that the change in curvature of the drop in response to the change in curvature of the substrate can be predicted from simple geometrical considerations, under the assumption that the drop's shape is a spherical cap, and that the volume remains unchanged through the curvature. The resulting prediction is in perfect agreement with the simulation results, for both convex and concave substrates. In addition, we calculate the line tension, namely by fitting the contact angle for different size drops to the modified Young equation. We find that the line tension for concave surfaces is larger than for convex surfaces, while for zero curvature it has a clear maximum. This feature is found to be correlated with the number of particles in the first layer of the liquid on the surface

Effects of heterogeneity on the drag force in random arrays of spheres

The modelling of the gas-solid interaction is a prerequisite in order\ud to accurately predict fluidized bed behaviour using models\ud such as the Discrete Particle Model (DPM) or the Two Fluid\ud Model (TFM). Currently, the drag force is usually modelled\ud purely based on porosity and slip velocity, which are averaged\ud with respect to the grid size used to solve the model equations.\ud Interfaces at heterogenous structures such as bubbles or free\ud board are not accounted for. As recently pointed out by Xu\ud et al. (2007), sub-grid information for the particle position is\ud available in DPM simulations, thus the local porosity is known\ud and can be used when calculating the drag.\ud Direct Numerical Simulation of flow in particulate systems\ud were done using the lattice Boltzmann method. These simulations\ud were carried out with random arrays of spheres which\ud only have a slight degree of heterogeneity and the gas-solid interaction\ud force on each particle was measured. First we compared\ud these results, which can be considered as the “true drag\ud force, with the drag force one would predict from a correlation\ud typically used in larger scale models (such as the relation of\ud van der Hoef et al. (2005)). Even for the random arrays, the\ud drag on some individual particles differed considerably (up to\ud 40%) from the predicted drag. Then we evaluate the effectiveness\ud of improved drag models, that use information on local\ud porosit

Simulation of density segregation in vibrated beds

We have investigated by numerical simulation the density segregation of fine equal-sized bronze and glass particles subject to vertical vibrations. The model was found to be capable of predicting the two main segregation forms (“bronze on top” and “sandwich”) in roughly the same regions of the phase diagram as was found experimentally by Burtally et al. We investigated the effects of pressure air forcing, friction and restitution of kinetic energy in collisions, and box size on the segregation behavior. We find that next to the interstitial air friction also has a large influence on the formation of the sandwich structure