Moving load on elastic structures: Passage through the wave speed barriers

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The asymptotic behaviour of an elastically supported infinite string and an elastic isotropic half plane (in frames of specific asymptotic model) under a moving point load are studied. The main results of this work are uniform asymptotic formulae and the asymptotic profile for the string and the exact solution and uniform asymptotic formulae for a half plane. The crucial assumption for both structures is that the acceleration is sufficiently small. In order to describe asymptotically the oscillations of an infinite string auxiliary canonical functions are introduced, asymptotically analyzed and tabulated. Using these functions uniform asymptotic formulae for the string under constant accelerating and decelerating point loads are obtained. Approximate formulae for the displacement in the vicinity of the point load and the singularity area behind the shock wave using the steady speed asymptotic expansion with additional contributions from stationary points where appropriate are derived. It is shown how to generalise uniform asymptotic results to the arbitrary acceleration case. As an example these results are applied for the case of sinusoidal load speed. It is shown that the canonical functions can successfully be used in the arbitrary acceleration case as well. The graphical comparative analysis of numerical solu- tion and approximations is provided for different moving load speed intervals and values of the parameters. Vibrations of an elastic half plane are studied within the framework of the asymp- totic model suggested by J. Kaplunov et al. in 2006. Boundary conditions for the main problem are obtained as a solution for the problem of a string on the surface of a half plane subject to uniformly accelerated moving load. The exact solution over the interior of the half plane is derived with respect to boundary conditions. Steady speed and Rayleigh wave speed asymptotic expansions are obtained. In the neighborhood of the Rayleigh speed the uniform asymptotic formulae are derived. Some of their interesting properties are discovered and briefly studied. The graphical comparative analysis of the exact solution and approximations is provided for different moving load speed intervals and values of the parameters.Studentship from Brunel Universit

A Note on Quasi-Triangulated Graphs

A graph is quasi-triangulated if each of its induced subgraphs has a vertex which is either simplicial (its neighbors form a clique) or cosimplicial (its nonneighbors form an independent set). We prove that a graph G is quasi-triangulated if and only if each induced subgraph H of G contains a vertex that does not lie in a hole, or an antihole, where a hole is a chordless cycle with at least four vertices, and an antihole is the complement of a hole. We also present an algorithm that recognizes a quasi-triangulated graph in O(nm) time

Mixed interval hypergraphs

AbstractWe investigate the coloring properties of mixed interval hypergraphs having two families of subsets: the edges and the co-edges. In every edge at least two vertices have different colors. The notion of a co-edge was introduced recently in Voloshin (1993, 1995): in every such a subset at least two vertices have the same color. The upper (lower) chromatic number is defined as a maximum (minimum) number of colors for which there exists a coloring of a mixed hypergraph using all the colors.We find that for colorable mixed interval hypergraph H the lower chromatic number χ(H) ⩽ 2, the upper chromatic number χ(H) = |X|−s(H), where s(H) is introduced as the so-called sieve number. A characterization of uncolorability of a mixed interval hypergraph is found, namely: such a hypergraph is uncolorable if and only if it contains an obviously uncolorable edge.The co-stability number α.√(H) is the maximum cardinality of a subset of vertices which contains no co-edge. A mixed hypergraph H is called co-perfect if χ(H′) = α√(H′) for every subhypergraph H′. Such minimal non-co-perfect hypergraphs as monostars and cycloids Cr2r−1 have been found in Voloshin (1995). A new class of non-co-perfect mixed hypergraphs called covered co-bi-stars is found in this paper. It is shown that mixed interval hypergraphs are coperfect if and only if they do not contain co-monostars and covered co-bi-stars as subhypergraphs.Linear time algorithms for computing lower and upper chromatic numbers and respective colorings for this class of hypergraphs are suggested

Pseudo-chordal mixed hypergraphs

AbstractA mixed hypergraph contains two families of subsets: edges and co-edges. In every coloring any edge has at least two vertices of different colors, any co-edge has at least two vertices of the same color. The minimum (maximum) number of colors for which there exists a coloring of a mixed hypergraph H using all the colors is called lower (upper) chromatic number. A mixed hypergraph is called uniquely colorable if it has exactly one coloring apart from the permutation of colors. A vertex is called simplicial if its neighborhood induces a uniquely colorable mixed hypergraph. A mixed hypergraph is called pseudo-chordal if it can be decomposed by consecutive elimination of simplicial vertices. The main result of this paper is to provide a necessary and sufficient condition for a polynomial to be a chromatic polynomial of a pseudo-chordal mixed hypergraph

Coloring mixed hypergraphs: from combinatorics to philosophy

We survey recent results and open problems on the chromatic spectrum,planarity and colorability of mixed hypergraphs and their relations to suchcategories of philosophy as identity and difference

About perfection of circular mixed hypergraphs

A mixed hypergraph is a triple H = (X,C,D), where X is the vertex set and each of C and D is a family of subsets of X, the C-edges and D-edges, respectively. A proper k-coloring of H is a mapping c : X → {1,...,k} such that each C-edge has two vertices with a common color and each D-edge has two vertices with different colors. Maximum number of colors in a coloring using all the colors is called upper chromatic number χ ̄(H). Maximum cardinality of subset of vertices which contains no C-edge is C-stability number αC (H). A mixed hypergraph is called C-perfect if χ ̄ (H') = αC (H') for any induced subhypergraph H'. A mixed hyper- graph H is called circular if there exists a host cycle on the vertex set X such that every edge (C- or D-) induces a connected subgraph on the host cycle. We give a characterization of C-perfect circular mixed hypergraphs

A note on the colorability of mixed hypergraph using k colors

The colorability problem on mixed hypergraphs is discussed. A criterion of colorability of mixed hypergraph with k colors is given

Diffuse retro-reflective imaging for improved mosquito tracking around human baited bednets

Robust imaging techniques for tracking insects have been essential tools in numerous laboratory and field studies on pests, beneficial insects and model systems. Recent innovations in optical imaging systems and associated signal processing have enabled detailed characterisation of nocturnal mosquito behaviour around bednets and improvements in bednet design, a global essential for protecting populations against malaria. Nonetheless, there remain challenges around ease of use for large scale in situ recordings and extracting data reliably in the critical areas of the bednet where the optical signal is attenuated. Here we introduce a retro-reflective screen at the back of the measurement volume, which can simultaneously provide diffuse illumination, and remove optical alignment issues whilst requiring only one-sided access to the measurement space. The illumination becomes significantly more uniform, although, noise removal algorithms are needed to reduce the effects of shot noise particularly across low intensity bednet regions. By systematically introducing mosquitoes in front and behind the bednet in lab experiments we are able to demonstrate robust tracking in these challenging areas. Overall, the retro-reflective imaging setup delivers mosquito segmentation rates in excess of 90% compared to less than 70% with back-lit systems

Eastern Vector of Russian State Policy Development for Ensuring Energy Security

This article is dedicated to the current problem of forming the Eastern vector of oil and gas policy within new energy policy and modern circumstances. The main goal of the work is to study the energy relations between Russia and the countries of the Asia-Pacific region, namely China. Using the analysis method, authors have highlighted the threats and possibilities of the influence of the current situation in the fuel and energy complex on Russia's energy security. Analysis of the existing situation on the global energy market has revealed that deepening and expansion of partnerships in economic and energy sphere with China are of interest to Russia as a Eurasian state. The basis for a partnership is a cooperation, based on China's demand for natural resources, while Russia will benefit from using effective innovation models of modernisation. Keywords: Asia-Pacific Region, Energy Sphere, Oil and Gas Policy, Raw Material Resource Potential, Energy Security, Energy Dialogue. JEL Classifications: P48, Q40