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Abstract: In this introductory note we define the concept of left almost polygroup and provide several examples. We also discuss the quotient structure and isomorphism theorems for left almost polygroups.
Keywords: left almost polygroup, direct product, hyperorder, homomorphism
Published in RUNG: 28.03.2018; Views: 3776; Downloads: 0
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Abstract: In spite of the successes of observational astro- and particle physics and cosmology very much of the universe remains unknown. The Standard Model of particle physics is a theory describing the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. But there is overwhelming evidence, that all the known particles, the ordinary (baryonic) matter, the building blocks of planets, stars and ourselves, only make up about 4.9% of the energy content of the universe. The standard model of cosmology (CDM) indicates that the total mass-energy of the universe contains beside the 4.9% ordinary matter two other components: 26.8% dark matter and 68.3% dark energy. The accelerating expansion of the Universe is the result of the effect of the dark energy with its most simple form given by a cosmological constant in Einstein's Equation. Dark matter is an unidentified type of matter that is not accounted for by dark energy and neutrinos and is generally believed to be a non-relativistic, charge neutral and non-baryonic new form of matter. Although dark matter has not been directly observed yet, its existence and properties are inferred from its gravitational effects such as the motions of visible matter, gravitational lensing, its influence on the universe's large-scale structure, and its effects in the cosmic microwave background. Thus the search for Dark Matter is the search for physics beyond the standard model. Although the nature of dark matter is yet unknown, its presence is crucial to understanding the future of the universe. The CRESST experiment is searching for direct evidence in the form of a nuclear recoil induced on a scintillating CaWO4 crystal by a dark matter particle, and is installed and taking data underground at Laboratory Nazionali del Gran Sasso (LNGS) in Italy. While both, dark energy and dark matter, have not been detected directly, a class of dark matter particles that interact only via gravity and the weak force, referred to asWeakly Interacting Massive Particles (WIMPs), has been established as the leading candidate among the dark matter community. For this thesis a special model of dark matter was studied, namely the dark photon. This thesis provides a detailed description of the calculation of the 90% upper limit on the dark photon kinetic mixing based on data from the second phase of the CRESST experiment. The analysis was carried out in a frequentist approach based on the (unbinned) maximum-likelihood method and likelihood ratios. To make a statement about the calculated result and its quality, the used algorithm had to be tested, what was done with Monte Carlo simulations (pseudo data).
Keywords: astro physics, particle physics, cosmology, universe, Standard Model of particle physics, standard model of cosmology, matter, ordinary matter, dark matter, dark energy, accelerating expansion of the Universe, non-baryonic, new form of matter, gravitational lensing, cosmic microwave background, search for physics beyond the standard model, CRESST experiment, direct detection, CaWO4 crystal, underground laboratory, Laboratory Nazionali del Gran Sasso, Weakly Interacting Massive Particles, WIMP, dark photon, 90% upper limit, upper limit, kinetic mixing, frequentist approach, unbinned, maximum likelihood
Published in RUNG: 13.10.2017; Views: 4598; Downloads: 0
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Abstract: The aim of this dissertation is to devise a meshless model describing the thermomechanical phenomena, which occur during DC casting of aluminium alloys under the influence of electromagnetic stirring. The thermoemchanical phenomena are important, because they can cause several type of defects, which can significantly deteriorate the quality of the resulting billet. The two most important of them are the hot tearing, which causes cracks to appear in the mushy zone, and the porosity, which demonstrates itself as micrometer sized voids in the microstructure of the billet. To calculate the stresses and strains, a computational model of the stationary state of the process, stated in axial symmetry, is formulated. It uses Eulerian formulation by fixing the computational domain to the mold of the casting device allowing the material to move through the computational domain. The stresses are calculated from the stress equilibrium equations. The small strain approximation is used to consider the three contributions to strain. The strain consists of the thermal strain, which is caused by the inhomogeneous thermal profile in the billet, the viscoplastic strain, which is caused by the irreversible deformation because of the large stresses occurring in the billet, and the elastic strain. The spatial discretization of the governing equations is performed by local radial basis function collocation method (LRBFCM) and the temporal discretization is achieved by the method of lines with implicit Euler formula. The method used for spatial discretization uses radial basis functions augmented by monomials to approximate the solution values on localized stencils. This approximation is used to construct the discretization coefficients of the differential operators present in the model. A flexible framework for formulation of multiphysics problems is developed to use the obtained discretization coefficients to construct the temporal discretization of the governing equations. The node arrangement, on which the spatial discretization is performed, was generated by a point-repel algorithm. The performance of the method is tested on several benchmark test cases. The accuracy of the discretization is estimated by comparing the analytic and the numerical solution to several stationary problems in thermomechancis. Of special interest is the performance of the method with respect to the choice of the shape parameter, which determines the spatial scale of the radial basis functions. Besides this, the dependence of the condition number of the interpolation matrix on the shape parameter is studied. The condition number is found fit to replace the condition number as the shape-determining free parameter of the method. The implementation of the solver of time dependent problems is tested on problem of thermoelasticity, which couples the thermal transport with the elastic waves. The results of the problem are compared with the finite element method, showing good agreement of the two methods. The results are also compared with the results obtained by meshless local Petrov-Galerkin method and the proposed local collocation method demonstrated significantly better solution quality in the studied case. The performance of the solver used to solve the system of nonlinear equations given by the viscoplastic constitutive equations is estimated on a quasi zero-dimensional problem. The results are found to match perfectly. Solution of a more complicated problem is obtained with the proposed method and the finite-element method, both methods giving practically the same solution, although some serious limitations of the chosen finite element solver are exposed during the selection of the problem parameters. Finally, the devised method is applied to the problem of DC casting of aluminium alloys. The thermomechanical model relies on a model of heat and mass transfer to obtain the input fields needed in the solver. The required fields are: temperature, pressure, liquid
Keywords: thermomechanics, viscoplasticity, aluminium alloys, direct-chill casting, electromagnetic stirring, hot tearing, porosity, meshless methods, local collocation method, radial basis functions, shape parameter
Published in RUNG: 28.06.2017; Views: 5886; Downloads: 255
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