Kink Chains from Instantons on a Torus

We describe how the procedure of calculating approximate solitons from instanton holonomies may be extended to the case of soliton crystals. It is shown how sine-Gordon kink chains may be obtained from CP1 instantons on a torus. These kink chains turn out to be remarkably accurate approximations to the true solutions. Some remarks on the relevance of this work to Skyrme crystals are also made.Comment: latex 17 pages, DAMTP 94-7

Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Octahedral and dodecahedral monopoles

It is shown that there exists a charge five monopole with octahedral symmetry and a charge seven monopole with icosahedral symmetry. A numerical implementation of the ADHMN construction is used to calculate the energy density of these monopoles and surfaces of constant energy density are displayed. The charge five and charge seven monopoles look like an octahedron and a dodecahedron respectively. A scattering geodesic for each of these monopoles is presented and discussed using rational maps. This is done with the aid of a new formula for the cluster decomposition of monopoles when the poles of the rational map are close together

Design, fabrication and testing of sandwich panel decking use in road freight trailers

This paper investigates the potential of sandwich structures in the novel application of road freight trailer decking. Sandwich panels are developed to be lightweight replacements to conventional birch plywood hardwood decking, which is the norm in European road freight trailers. A tailored material selection process is used to identify the most advantageous sandwich panel material combinations with respect to flexural properties and material cost. Sandwich panels with woven glass fibre reinforced polyester and an end-grain balsa are found to be the most advantageous material combination in terms of both raw material cost and mechanical performance. These panels are fabricated using a single shot fabrication technique and are approximately 30% lighter than conventional birch plywood trailer decking. This weight saving corresponds to approximately 165 kg in a standard 13.6 m long European road freight trailer. Three point bend testing has shown that these sandwich panels have superior flexural strength and comparable flexural stiffness to birch plywood. Large panel testing confirmed that these panels can withstand roughly four times the forklift wheel load likely to be seen in-service. The shear properties of two grades of rigid end-grain balsa core are also studied to illustrate the importance of using a higher density balsa core. Practical considerations, such as joining and recyclability, for using sandwich panels in this application are also discussed.Centre for Sustainable Road Freight, Engineering and Physical Sciences Research Council (Grant ID: EP/K00915X/1

Reducing the energy consumption of heavy goods vehicles through the application of lightweight trailers: Fleet case studies

Reducing the empty weight of articulated heavy goods vehicle trailers is one avenue that needs to be explored in reducing the carbon footprint of the road freight industry as a whole. A statistical analysis of two heavy goods vehicle fleets operating in the United Kingdom has helped to identify double-deck trailers used in grocery haulage and 'walking-floor' trailers used in bulk haulage as two examples of trailers that can benefit significantly from lightweighting. Energy consumption of numerous articulated heavy goods vehicles is quantified through an idealised drive cycle analysis reflecting a long haul journey over a highway. This energy analysis allows for a mass energy performance index to be established. The analysis has shown that reducing the empty weight of trailers by 30% can cause reductions of up to 18% and 11% in mass energy performance index for double-deck trailers and 'walking-floor' trailers respectively. Using this approach, trailers that will benefit the most from weight reduction can be identified systematically, allowing for lightweighting strategies to be implemented more effectively. Strategies to reduce empty trailer weight and improve vehicle utilisation are also discussedThe authors would like to acknowledge the financial support from the members of the Centre for Sustainable Road Freight and from the Engineering and Physical Sciences Research Council (Grant Reference EP/K00915X/1).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.trd.2015.09.01

Symmetric Instantons and Skyrme Fields

By explicit construction of the ADHM data, we prove the existence of a charge seven instanton with icosahedral symmetry. By computing the holonomy of this instanton we obtain a Skyrme field which approximates the minimal energy charge seven Skyrmion. We also present a one parameter family of tetrahedrally symmetric instantons whose holonomy gives a family of Skyrme fields which models a Skyrmion scattering process, where seven well-separated Skyrmions collide to form the icosahedrally symmetric Skyrmion.Comment: 22 pages plus 1 figure in GIF forma

Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be translated into results about the dynamics of 3-monopoles. Using a numerical ADHMN construction we compute the monopole energy density at various points on two interesting geodesics. The first is a geodesic over the two-dimensional rounded cone submanifold corresponding to right angle scattering and the second is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit

Study of industrial titania synthesis using a hybrid particle-number and detailed particle model

We apply a hybrid particle model to study synthesis of particulate titania under representative industrial conditions. The hybrid particle model employs a particle-number description for small particles, and resolves complicated particle morphology where required using a detailed particle model. This enables resolution of particle property distributions under fast process dynamics. Robustness is demonstrated in a network of reactors used to simulate the industrial process. The detailed particle model resolves properties of the particles that determine end product quality and post-processing efficiency, including primary particle size and degree of aggregate cohesion. Sensitivity of these properties to process design choices is quantified, showing that higher temperature injections produce more sintered particles; more frequent injections narrow the geometric standard deviation of primary particle diameter; and chlorine dilution reduces particle size and size variance. Structures of a typical industrial particle are compared visually with simulated particles, illustrating similar aggregate features with slightly larger primary particles

Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis