3,834 research outputs found

    A Penrose polynomial for embedded graphs

    Get PDF
    We extend the Penrose polynomial, originally defined only for plane graphs, to graphs embedded in arbitrary surfaces. Considering this Penrose polynomial of embedded graphs leads to new identities and relations for the Penrose polynomial which can not be realized within the class of plane graphs. In particular, by exploiting connections with the transition polynomial and the ribbon group action, we find a deletion-contraction-type relation for the Penrose polynomial. We relate the Penrose polynomial of an orientable checkerboard colourable graph to the circuit partition polynomial of its medial graph and use this to find new combinatorial interpretations of the Penrose polynomial. We also show that the Penrose polynomial of a plane graph G can be expressed as a sum of chromatic polynomials of twisted duals of G. This allows us to obtain a new reformulation of the Four Colour Theorem

    The impact of Self-Generated Images in online pornography

    Get PDF
    This investigation seeks to evaluate the impact on individuals, and society, of Self-Generated Images (SGI’s) in online pornography. It presents an inquiry into the extent, and modes, of SGI use among a large sample of adult internet users. This form the initial platform for a theoretical analysis of the rapidly emerging topic, alongside an empirical investigation into how SGI’s are used, and criminally abused. A mixed research method strategy was consequently adopted, employing a quantitative anonymous online survey (Stage 1), qualitative face-to-face interviews with serving Metropolitan Police Service officers in the SOECA unit (Stage 2), and qualitative Skype interviews with active SGI users (Stage 3). The thesis is divided into three main sections. Firstly, in chapters one-to-four, the context for this study into SGI’s is explained, including the specific UK statute laws regarding licit and illicit pornographic images. Commonly used pornographic terminologies are defined. Furthermore, existent research on the topic of SGI’s/online pornography is scrutinized, and several theoretical issues are given a discourse in relation to SGI’s. An analysis of the free speech/online pornography debate is included, together with an examination of the criminal abuse of SGI’s. The second part, chapter five, provides a rationale for the adoption of a mixed research methods strategy in pursuing the aims of this study. Many methodological issues regarding the three stages of the primary fieldwork are addressed; these include: ontology, epistemology, research paradigms and axiology, ethical underpinnings, practical considerations, and the strengths and limitations of methods chosen. In the third section, chapters six-to-eight, the study’s key findings include a taxonomy of the six main types of SGI. Passive SGI viewing is very pervasive, particularly among the key demographic groups of younger adults, Lesbian Gay Bisexual Transgender (LGBT) and males, and may be becoming the norm. Free PornTube websites are predominately used; but also, increasingly, social network sites (SNS’s) and messaging/image sharing apps. Most adults use SGI’s safely for sexual stimulation; however, some use them for educational and humorous purposes. For a minority of active creators of SGI’s, disastrous personal consequences can result because of subsequent criminal abuse, including cyber-bullying/trolling, sextortion, etc. Gay and bisexual men have highly accelerated rates of SGI use on hooking-up sites, often leading to hazardous risk taking. Children face grave dangers from making and sharing sexualised SGI’s as online child sexual abuse (CSA), grooming and sextortion, etc. may transpire. In the UK’s schools, Personal, Social and Health Education (PSHE), and Sex and Relationships Education (SRE), are in a parlous state regarding the issues and dangers of SGI’s. Finally, this inquiry provides some original insights into the areas of applying and generating theories, using mixed research methods, and the empirical findings uncovered

    Clyde superficial deposits and bedrock models released to the ASK Network 2013 : a guide for users

    Get PDF
    This report draft provides an overview of the Clyde superficial deposits models to be released in 2013 and detail on the Central Glasgow Superficial Deposits Model currently released to the ASK network. The geological models are an interpretation of digital datasets held by the British Geological Survey. A summary of the construction and limitations of the models and a brief description of the modelled units is given. The report will be updated and revised as more models become available for release to the ASK network. More details on the models can be found in the previous reports Merritt et al. (2009), Monaghan (2012a) and Monaghan et al. (2012)

    Controlling Artificial Viscosity in SPH simulations of accretion disks

    Get PDF
    We test the operation of two methods for selective application of Artificial Viscosity (AV) in SPH simulations of Keplerian Accretion Disks, using a ring spreading test to quantify effective viscosity, and a correlation coefficient technique to measure the formation of unwanted prograde alignments of particles. Neither the Balsara Switch nor Time Dependent Viscosity work effectively, as they leave AV active in areas of smooth shearing flow, and do not eliminate the accumulation of alignments of particles in the prograde direction. The effect of both switches is periodic, the periodicity dependent on radius and unaffected by the density of particles. We demonstrate that a very simple algorithm activates AV only when truly convergent flow is detected and reduces the unwanted formation of prograde alignments. The new switch works by testing whether all the neighbours of a particle are in Keplerian orbit around the same point, rather than calculating the divergence of the velocity field, which is very strongly affected by Poisson noise in the positions of the SPH particles.Comment: 8 pages, 5 figure

    Comparison of C═C bond hydrogenation in C-4 unsaturated nitriles over Pt/alumina

    Get PDF
    The hydrogenation of allyl cyanide (but-1-ene-4-nitrile, AC), trans- and cis-crotononitrile (E- and Z-but-2-ene nitrile, TCN and CCN), and methacrylonitrile (2-cyano-1-propene, MCN) were studied, both singly and competitively, over a Pt/alumina catalyst in the liquid phase. Each unsaturated nitrile only underwent C═C bond hydrogenation: no evidence was found for the formation of the saturated or unsaturated amine. The nonconjugated allyl cyanide was found to be the most reactive unsaturated nitrile. Activation energies for the hydrogenation of the C═C bond in AC and MCN were determined giving values of 64 ± 7 kJ mol–1 for AC and 37 ± 4 kJ mol–1 for MCN. The reaction was zero order for both nitriles. Competitive hydrogenations revealed that not only does allyl cyanide react preferentially over the other isomers but also it inhibits the hydrogenation of the other isomers. When all four nitriles were simultaneously hydrogenated, inhibition effects were easily seen suggesting that in terms of strength of bonding to the surface an order of AC > CCN > TCN ∼ MN can be generated

    Unconventional energy resources in a crowded subsurface: reducing uncertainty and developing a separation zone concept for resource estimation and deep 3D subsurface planning using legacy mining data

    Get PDF
    Over significant areas of the UK and western Europe, anthropogenic alteration of the subsurface by mining of coal has occurred beneath highly populated areas which are now considering a multiplicity of ‘low carbon’ unconventional energy resources including shale gas and oil, coal bed methane, geothermal energy and energy storage. To enable decision making on the 3D planning, licensing and extraction of these resources requires reduced uncertainty around complex geology and hydrogeological and geomechanical processes. An exemplar from the Carboniferous of central Scotland, UK, illustrates how, in areas lacking hydrocarbon well production data and 3D seismic surveys, legacy coal mine plans and associated boreholes provide valuable data that can be used to reduce the uncertainty around geometry and faulting of subsurface energy resources. However, legacy coal mines also limit unconventional resource volumes since mines and associated shafts alter the stress and hydrogeochemical state of the subsurface, commonly forming pathways to the surface. To reduce the risk of subsurface connections between energy resources, an example of an adapted methodology is described for shale gas/oil resource estimation to include a vertical separation or ‘stand-off’ zone between the deepest mine workings, to ensure the hydraulic fracturing required for shale resource production would not intersect legacy coal mines. Whilst the size of such separation zones requires further work, developing the concept of 3D spatial separation and planning is key to utilising the crowded subsurface energy system, whilst mitigating against resource sterilisation and environmental impacts, and could play a role in positively informing public and policy debate
    corecore