Dissertations / Theses on the topic 'Ground loops'
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Myllylä, K. (Kari). "On the solvability of groups and loops." Doctoral thesis, University of Oulu, 2003. http://urn.fi/urn:isbn:9514269055.
Full textBauer, Sven. "Loops on real Stiefel-manifolds." Thesis, University of Aberdeen, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367371.
Full textPacheco, Rui. "Harmonic maps and loop groups." Thesis, University of Bath, 2004. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.404621.
Full textZhou, Yongxin. "Alternative algebras and RA loops." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0002/NQ42490.pdf.
Full textSouaid, Charbel. "Identification and characterization of Polycomb repressed gene-enhancer loops." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS015.
Full textIn the mouse embryonic stem cells (mESCs), Polycomb Group Proteins (PcG) repress developmental genes and thereby participating in the maintenance of the pluripotency. PcG repress genes by depositing the H3K27me3 histone marks on their regulatory elements, followed by chromatin compaction. In addition to the H3K27me3 marks, those genes carry H3K4me3 active marks and were characterized as bivalent. Intriguingly, at many PcG repressed genes, DNA loops can be observed with enhancer elements, which are normally thought to have an activating function. The aim of my project is to both describe and mechanistically dissect the function of Polycomb repressed promoter – enhancer loops.During my PhD, I aimed firstly to identify all promoter–enhancer loops involved by PcG repressed genes in mESCs. I have performed ChIP-seq profiling of 4 histone marks and identified around 2500 PcG repressed promoters and 13000 enhancers. Using a recently published high-resolution Hi-C data in mESCs, I have identified all DNA loops that are formed by PcG repressed promoters. Surprisingly, a high percentage of bivalent promoters were found to contact active enhancers. The presence of those loops were validated by ultra-high 4C-seq on selected genes and imply a small significant increase of the gene expression without leading to a complete activation of the gene. I have established a more physiological ESC model (2i+VitC) where H3K27me3 is reduced at all promoters. I have performed ChIP-seq, where bivalent promoters were all classified as H3K27me3 negative. RNA-seq experiments have showed that those genes do not become activated. 4C-seq experiments have revealed that those loops do not disappear after PcG removal, whereas the half of interacted enhancer loose their H3K27ac active marks. Those genes seem to remain repressed by an unknown mechanism. These results argue for a possible role of PcG in preparing the gene for their activation by blocking the productivity of such DNA loops. Secondly, I aimed to functionally characterize those DNA loops by using a CRISPR/dCas9 approach to completely remove H3K27me3 from two PcG repressed genes that contact active enhancers Pax6 and Nkx1-1 genes. This system is still under optimization steps.My project revealed the most systematic characterization of DNA loops under the regulation of PcG, providing important insight how PcG function to inactivate such loops. I have highlighted an additional function of PcG which the involvement in the repression of already establish loops between active enhancers and promoters and thereby blocking the productivity of such activating loops. This function is an addition to the already described repressive function of PcG on both promoters and poised enhancers
Kim, Yunhyong. "Smooth cochain cohomology of loop groups." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621575.
Full textRaynor, Sophia C. "Compact symmetric multicategories and the problem of loops." Thesis, University of Aberdeen, 2018. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=236493.
Full textKim, Jeong I. "Log-Periodic Loop Antennas." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/34392.
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Three prototype antennas were constructed and measured in the Virginia Tech Antenna Laboratory. Far-field patterns and input impedance were measured over a wide range of frequencies. The measured results agree well with the calculated results. Because of its wide bandwidth, high gain, and small size, the LPLA is expected to find applications as feeds for reflector antennas, as detectors in EMC scattering range, and as mobile communication antennas.
Master of Science
Blomqvist, Mikael. "Construction and evaluation of a magnetoresistive ground penetrating radar system." Thesis, Uppsala universitet, Ångström Space Technology Centre (ÅSTC), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-159904.
Full textAloi, Daniel N. "Electromagnetic analysis of ground multipath for satellite-based positioning systems." Ohio University / OhioLINK, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1178816934.
Full textBalbo, Pedro Paulo Abel. "Teoremas de Sylow para loops de Moufang." reponame:Repositório Institucional da UFABC, 2016.
Find full textDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2016.
Neste trabalho foram abordados os Teoremas de Sylow para loops de Moufangnitos. A validade destes teoremas nocontexto não associativo não ocorre de maneira direta uma vez que o menor loop deMoufang finito simples tem ordem 120 e não possui subloop de ordem 5. Foi analisada aaplicação destes teoremas para duas categoriasde loops de Moufang de ordem par: os loops de Cheine os loops de Paige. Para os loops de Chein vemos que dois subloops de Sylow são conjugados. Para os loops de Paige P(q) vericamos a existência e o númerode p-subloops de Sylow.
In this work Sylow's theorems for nite Moufang loops were investigated. The validity of these theorems in a non-associative context does not occur directly as the smallest simple nite Moufang loop hasorder 120 and contains no subloopo forder 5. We analyzed the application of these theorems for two categories of Moufang loops of even order: Chein loop sand Paige loops.For Chein loops we can see that any two Sylow's sub loop sare always conjugated. For Paige loops P(q) we verifed the existence of p-Sylow subloops and studied their number.
Pittman-Polletta, Benjamin Rafael. "Factorization in unitary loop groups and reduced words in affine Weyl groups." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/194348.
Full textSwoboda, Jan. "The Yang-Mills gradient flow and loop groups /." Zürich : ETH, 2009. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=18296.
Full textSadasue, Gaku. "Equivalence-Singularity dichotomy for the Wiener measures on path groups and loop groups." 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/181092.
Full textSoh, Mun Lok Bernard. "Hardware in the loop implementation of adaptive vision based guidance law for ground target tracking." Thesis, Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Dec/08Dec%5FSoh.pdf.
Full textThesis Advisor(s): Dobrokhodov, Vladimir N. ; Jones, Kevin D. "December 2008." Description based on title screen as viewed on February 2, 2009. Includes bibliographical references (p. 89-90). Also available in print.
Anjos, Giliard Souza dos. "Half-Isomorfismos de loops automórficos." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-03052018-221550/.
Full textAutomorphic loops, or A-loops, are loops in which every inner mapping is an automorphism. This variety of loops includes groups and commutative Moufang loops. Dihedral automorphic loops form a class of A-loops, constructed from the duplication of finite abelian groups, that generalizes the construction of the dihedral group. Another class of A-loops is the Lie automorphic loops, constructed from Lie rings, where a new operation between its elements is defined. A half-isomorphism is a bijection f between loops L and L\' where, for any x and y belong to L, we have that f(xy) belongs to the set {f(x)f(y),f(y)f(x)}. We say that half-isomorphism f is non trivial when f is neither an isomorphism nor an anti-isomorphism. In this thesis, we describe properties of half-isomorphisms of loops, we classify the half-isomorphisms between dihedral automorphic loops and we obtain the group of half-automorphisms in this class. For the Lie automorphic loops of odd order, we show that every half-automorphism is trivial.
Bergeron-Legros, Gabriel. "Weil Representation and Central Extensions of Loop Symplectic Groups." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31516.
Full textReis, Márcio Alexandre de Oliveira. "Loops de Bol algébricos e analíticos." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-27062010-143306/.
Full textIn this work, we classify up to isomorphism, the Bol algebras of dimension 2 over a eld of characteristic 0. We also determine their enveloping Lie algebras and we exhibit two non-isomorphic Bol algebras which have isomorphic enveloping Lie algebras. We determine the (local) correspondent algebraic groups of each of those enveloping Lie algebras and we show that every global analytic (algebraic) Bol loop of dimension 2 over a eld of characteristic 0 is a group. We exhibit examples of non-nilpotent solvable algebraic Bol loops in dimension n for every n > 2, and we were able to give a necessary and sucient condition to decide if a local algebraic Bol loop is global when its enveloping Lie algebra is nilpotent of index 2 and char(F) 6= 2:
Hughes, Kyle L. "Commercial Program Development for a Ground Loop Geothermal System: G-Functions, Commercial Codes and 3D Grid, Boundary and Property Extension." Wright State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1324332345.
Full textDamiani, Céleste. "The topology of loop braid groups : applications and remarkable quotients." Caen, 2016. http://www.theses.fr/2016CAEN2021.
Full textIn this these we study loop braid groups, we explore some of their topological applications and some remarquable quotients. The thesis is composed by four parts:- Unifying the different approaches to loop braid groups. Several formulations are being used by researchers working with loop braid groups in different fields; we present these interpretations and prove their equivalence. - A topological version of Markov’s theorem for ribbon torus-links. Using the understanding of the interpretation of loop braids as knotted objects in the 4-dimensional space, we give a topological proof of a version of Markov theorem for loop braids with closure in a solid torus in the 4-dimensional space. - Alexander invariants for ribbon tangles. We define an Alexander invariant on ribbon tangles. From this invariant we extract a functorial generalization of the Alexander polynomial. This invariant has a deep topological meaning, but lacks a simple way of computation. To overcome this problem we establish a correspondence with Archibal’s multivariable Alexander polynomial for tangles. - Quotients of the virtual braid group. We study the groups of unrestricted virtual braids, a family of quotients of the loop braid groups, and describe their structure. As a consequence we show that any fused link admits as a representative the closure of a pure unrestricted virtual braid
Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.
Full textNew, Stephen J. H. "Hamiltonian systems and loop groups applied to equations of KdV type." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60055.
Full textOzel, Cenap. "On the complex cobordism of flag varieties associated to loop groups." Thesis, University of Glasgow, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241783.
Full textReilly, Nicholas James. "Cmos Programmable Time Control Circuit Design For Phased Array Uwb Ground Penetrating Radar Antenna Beamforming." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/687.
Full textGross, Paul A. II. "Commercial Program Development for a Ground Loop Geothermal System: Energy Loads, GUI, Turbulent Flow, Heat Pump Model and Grid Study." Wright State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1324258915.
Full textPallekonda, Seshendra. "Bounded category of an exact category." Diss., Online access via UMI:, 2008.
Find full textFilho, Antonio Calixto de Souza. "Sobre uma classificação dos anéis de inteiros, dos semigrupos finitos e dos RA-loops com a propriedade hiperbólica." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-30012009-163028/.
Full textFor a given division algebra of a quaternion algebra, we construct and define two types of units of its $\\Z$-orders: Pell units and Gauss units. Also, for the quadratic imaginary extensions over the racionals and some fixed group $G$, we classify the algebraic integral rings for which the unit group ring is a hyperbolic group. We also classify the finite semigroups $S$, for which all integral orders $\\Gamma$ of $\\Q S$ have hyperbolic unit group $\\U(\\Gamma)$. We conclude with the classification of the $RA$-loops $L$ for which the unit loop of its integral loop ring does not contain a free abelian subgroup of rank two.
Biswas, Arindam. "Théorie des groupes approximatifs et ses applications." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS573.
Full textIn the first part of this thesis, we study the structure of approximate subgroups inside metabelian groups (solvable groups of derived length 2) and show that if A is such a K-approximate subgroup, then it is K^(O(r)) controlled (in the sense of Tao) by a nilpotent group where r denotes the rank of G=Fit(G) and Fit(G) is the fitting subgroup of G.The second part is devoted to the study of growth of sets inside GLn(Fq) , where we show a bound on the diameter (with respect to any set of generators) for all finite simple subgroups of this group. What we have is - if G is a finite simple group of Lie type with rank n, and its base field has bounded size, then the diameter of the Cayley graph C(G; S) would be bounded by exp(O(n(logn)^3)). If the size of the base field Fq is not bounded then our method gives a bound of q^(O(n(log nq)3)) for the diameter.In the third part we are interested in the growth of sets inside commutative Moufang loops which are commutative loops respecting the moufang identities but without (necessarily)being associative. For them we show that if the sizes of the associator sets are bounded then the growth of approximate substructures inside these loops is similar to those in ordinary groups. In this way for the subclass of finitely generated commutative moufang loops we have a classification theorem of its approximate subloops
Davis, Aaron Charles, and aaron davis@rmit edu au. "Quantitative Characterisation of Airborne Electromagnetic Systems." RMIT University. Applied Physics, 2007. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080723.103030.
Full textGavira, Romero Alberto. "Cellular approximations of infinite loop spaces and classifying spaces." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/133278.
Full textGiven a pointed topological space A, in 1995 E. Dror-Farjoun introduced the notion of A-homotopy, where A and its suspensions play the same role of the spheres in classical homotopy. Therefore the A-homotopy groups of a pointed space X are defined as the homotopy classes of maps from the suspensions of A to X. The idea of CW-complex is replaced by the one of A-cellular space, i.e., a space constructed by certain iterated homotopy colimits from A. The concept of cellular approximation is replaced by the A-cellular approximation, this is, a space A-cellular CWAX together with a natural map CWAX → X which induces an equivalence in the mapping spaces map*(A, CWAX) and map*(A, X), and hence an isomorphism in A-homotopy groups. Let p be a prime. In this work we study the A-cellularization, where A is a classifying space of type BZ/pm, BZ/p∞, or a product of these, of two families of spaces: the ΣBZ/p-acyclic spaces up to p-completion and the classifying spaces of p-local compact groups. In the first case we prove that the A-cellularization of a 1-connected ΣBZ/p-acyclic space up to p-completion X is equivalent to the homotopy fibre of the rationalization X^p → (X^p)Q.. Examples include the 1-connected infinite loop spaces and Postnikov pieces whose second homotopy group is a torsion group. In the second case, given a p-local group compact (S, F , L ), for the study of the A-cellularization of |L |^p, we define the kernel of a map f : |L |^p → Y^ as the subgroup of S formed by the elements x which the restriction of f to the classifying space of the group generated by x is null-homotopic. Under certain assumptions on |L |^p, we show that if the kernel of a certain map, which is determinant in the computation of the A-cellularization, is the p-group S, then the A-cellularization of |L |^p is the homotopy fibre of the rationalization |L |^p → (|L |^p)Q. In the finite case we are more precise, we prove that if (S, F , L ) is a finite p- local group, then |L |^p is BZ/pm-cellular if and only if the kernel of this map is equal to the minimal strongly F -closed subgroup in S that contains all the pi-torsion for i ≤ m. In the case of a compact Lie group, we prove that there is a non-negative integer m0 such that for all m ≥ m0, the (BZ/p∞ x BZ/pm)-cellularization of BG^p is equivalent to the homotopy fibre of the rationalization BG^p → (BG^p)Q.
Takata, Doman. "A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds." Kyoto University, 2018. http://hdl.handle.net/2433/232217.
Full textHelmreich, Peter [Verfasser], Karl-Hermann [Akademischer Betreuer] Neeb, and Karl-Hermann [Gutachter] Neeb. "A Convexity Theorem for Twisted Loop Groups / Peter Helmreich ; Gutachter: Karl-Hermann Neeb ; Betreuer: Karl-Hermann Neeb." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2020. http://d-nb.info/1223708233/34.
Full textMukai, Daichi. "Mirror symmetry of nonabelian Landau-Ginzburg orbifolds with loop type potentials." Kyoto University, 2020. http://hdl.handle.net/2433/253068.
Full textBillings, Don, Mei Wei, Joseph Leung, Michio Aoyagi, Fred Shigemoto, and Rob Honeyman. "REAL-TIME INTEGRATION OF RADAR INFORMATION, AND GROUND AND RADIOSONDE METEOROLOGY WITH FLIGHT RESEARCH DATA." International Foundation for Telemetering, 1998. http://hdl.handle.net/10150/607368.
Full textAlthough PCM/TDM framed data is one of the most prevalent formats handled by flight test ranges, it is often required to acquire and process other types. Examples of such non-standard data types are radar position information and meteorological data from both ground based and radiosonde systems. To facilitate the process and management of such non-standard data types, a micro-processor based system was developed to acquire and transform them into a standard PCM/TDM data frame. This obviated the expense of developing additional special software and hardware to handle such non-standard data types.
Renard, Sylvain. "Validation «Hardware in the loop » de l’architecture de commande embarquée du groupe moto-propulseur hybride pour véhicules industriels." Lyon, INSA, 2008. http://theses.insa-lyon.fr/publication/2008ISAL0131/these.pdf.
Full text[The development of vehicles less polluting leads to more complex electronic architectures related to the powertrain, which increases the risk of failure. The main objective of our work is to develop a HIL (Hardware In the Loop) simulation platform in order to verify the electronic system compliance, in charge of a parallel hybrid powertrain management, in relation to its specifications. From verification plans analysis, we have defined a method to build a specification booklet for the HIL platform development; the aim was to define the necessary area and the type of the required modelling to cover the complete verification plan. A special care has been brought in the development of the models of electrical machine, DC/AC converter or gearbox with the help of bond graph language. The efficiency of this method has been proved with the effective achievement of ECU verification plans. . ]
Inahama, Yuzuru. "Logarithmic Sobolev Inequality on Free Loop Groups for Heat Ker-nel Measures Associated with the General Sobolev Spaces." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/150808.
Full textPranzetti, Daniele. "TQFT and Loop Quantum Gravity : 2+1 Theory and Black Hole Entropy." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10032.
Full textThis thesis work concentrates on the non-perturbative canonical approach to the formulation of a quantum theory of gravity in the framework of Loop Quantum Gravity (LQG), addressing two major problems. In the first part, we investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of non-vanishing cosmological constant and try to make contact with alternative quantization approaches already existing in the literature. In the second part, we concentrate on a very important application of LQG: the definition and the counting of microstates of a statistical mechanical ensemble which provides a description and accounts for the black hole entropy. Our analysis strongly relies on and extends to a manifestly SU(2) invariant treatment the seminal work of Ashtekar et al
Wuttke, Sebastian. "Some aspects of the Wilson loop." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2015. http://dx.doi.org/10.18452/17225.
Full textThis thesis is motivated by the AdS/CFT correspondence and the duality between gluon scattering amplitudes and light-like polygonal Wilson loops in N=4 super Yang-Mills theory. At strong coupling light-like polygonal Wilson loops and gluon scattering amplitudes have a description in terms of space-like minimal surfaces in AdS5. We use a Pohlmeyer reduction to derive a classification of all space-like minimal surfaces in AdS3xS3 that have flat projections. The classification consists of nine different classes and contains space-like, time-like and degenerated AdS3 projections. For solutions that admit a closed light-like polygonal boundary we calculate the regularized area. At weak coupling light-like polygonal Wilson loops and gluon scattering amplitudes obey the BDS Ansatz corrected by a remainder function. We present a renormalisation group equation technique using self-crossing Wilson loops to extract the divergences of the remainder function in this limit. Using this technique we analyse two different types of self-crossing. We present the leading and sub-leading divergences up to four loops for a crossing between two edges and the leading divergences for a crossing between two vertices. For a crossing between two edges we present an analytic continuation to the euclidean regime to predict certain terms that have to occur in the unknown analytic expression of the remainder function.
Rappel, Valentin Maximilian [Verfasser], Peter [Gutachter] Littelmann, and Ghislain [Gutachter] Fourier. "The path model and Bott–Samelson manifolds in the context of loop groups / Valentin Maximilian Rappel ; Gutachter: Peter Littelmann, Ghislain Fourier." Köln : Universitäts- und Stadtbibliothek Köln, 2021. http://d-nb.info/1230059881/34.
Full textLano, Ralph Peter. "Application of co-adjoint orbits to the loop group and the diffeomorphism group of the circle." Thesis, University of Iowa, 1994. https://ir.uiowa.edu/etd/5393.
Full textKufa, Martin. "Planární fraktální filtr na substrátu s porušenou zemí." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2012. http://www.nusl.cz/ntk/nusl-219832.
Full textAbbas, Junaid. "Logical selectivity for medium voltage overcurrent protection and its verification via co-simulation tool for the responses of the power and communication network." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15274/.
Full textYoung, Nathan Lee. "Effect of Rivers on Groundwater Temperature in Heterogeneous Buried-Valley Aquifers: Extent, Attenuation, and Phase Lag of Seasonal Variation." Wright State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=wright1401813367.
Full textAldubyan, Mohammad Hasan. "Thermo-Economic Study of Hybrid Photovoltaic-Thermal (PVT) Solar Collectors Combined with Borehole Thermal Energy Storage Systems." University of Dayton / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1493243575479443.
Full textPellegrino, Gregory S. "Design of a Low-Cost Data Acquisition System for Rotordynamic Data Collection." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/1978.
Full textLumia, Luca. "Digital quantum simulations of Yang-Mills lattice gauge theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/22355/.
Full textPettersson, Anna, and Anna Larsson. ""There is no business on a dead planet" : En fallstudie av interna kommunikationsprocesser om hållbara arbetssätt i IT-konsultbranschen." Thesis, Uppsala universitet, Institutionen för informatik och media, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-416775.
Full textCarrozza, Sylvain. "Tensorial methods and renormalization in Group Field Theories." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112147/document.
Full textIn this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory.Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one hand,and to matrix models and tensor models on the other hand. They model quantum space-time, in the sense that their Feynman amplitudes label triangulations, which can be understood as transition amplitudes between LQG spin network states. The question of renormalizability is crucial if one wants to establish interesting GFTs as well-defined (perturbative) quantum field theories, and in a second step connect them to known infrared gravitational physics. Relying on recently developed tensorial tools, this thesis explores the GFT formalism in two complementary directions. First, new results on the large cut-off expansion of the colored Boulatov-Ooguri models allow to explore further a non-perturbative regime in which infinitely many degrees of freedom contribute. The second set of results provide a new rigorous framework for the renormalization of so-called Tensorial GFTs (TGFTs) with gauge invariance condition. In particular, a non-trivial 3d TGFT with gauge group SU(2) is proven just-renormalizable at the perturbative level, hence opening the way to applications of the formalism to (3d Euclidean) quantum gravity
Olsen, Peter A. "Shear Modulus Degradation of Liquefying Sand: Quantification and Modeling." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/1214.
Full textThürigen, Johannes. "Discrete quantum geometries and their effective dimension." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17309.
Full textIn several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.