subject:( 510)

1. Grapsas, Dionysios. Staggered fractional step numerical schemes for models for reactive flows : Schémas à mailles décalés pour des modèles d'écoulements compressible réactifs.

Degree: Docteur es, Mathématiques et informatique, 2017, Aix Marseille Université

URL: http://www.theses.fr/2017AIXM0566

►

On développe et analyse des schémas numériques de projection pour les écoulements réactifs. La discrétisation en espace est effectuée sur des maillages décalés. La première… (more)

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On développe et analyse des schémas numériques de projection pour les écoulements réactifs. La discrétisation en espace est effectuée sur des maillages décalés. La première partie aborde le côté hydrodynamique du problème et propose un schéma numérique pour les équations de Navier-Stokes compressible. Le schéma proposé possède au moins une solution et préserve les propriétés de stabilité du problème continu. Des test numériques confirment son bon comportement dans la limite non-visqueux incompressible ainsi que dans la limite d’Euler.On s’intéresse ensuite au calcul des écoulements compressible réactifs pour des fluides partiellement prémélangés. La discrétisation est basée sur un modèle qui utilise une équation différentielle du type level-set pour localiser le fron de flamme, couplée avec un système de lois de conservation. L’algorithme possède au moins une solution et préserve les bornes physiques des inconnues; de plus, toute suite de solutions approchées du système de lois de conservation converge (à une sous-suite près) vers une solution faible du problème continu. Dans le cas non-visqueux et pour des termes de réaction de plus en plus raides, le modèle doit dégénérer vers un modèle pour lequel la solution du problème de Riemann est établie. Des tests numériques confirment que c’est bien le cas.La dernière partie traite la discrétisation d’un système de lois de conservation, qui modélise l’écoulement réactif généré par la combustion de poussières, à faible nombre de Mach et en une dimension d’espace. Ce modèle comporte des termes de diffusion massique assez génériques. L’algorithme préserve par construction les propriétés de stabilité du problème continu.

We develop and analyze fractional step numerical schemes for reactive flows. The space discretization is staggered.The first part deals with the purely hydrodynamical part of the problem and proposes a numerical scheme for the compressible Navier-Stokes equations. The scheme is shown to have at least one solution and to preserve the stability properties of the continuous problem. Numerical tests confirm its potentialities, both in the viscous incompressible and Euler limits.Then we turn to the computation of partially premixed compressible reactive flows. The physical model uses a level-set-like partial differential equation to localize the flame front, coupled with the system of balance laws. The scheme is shown to possess at least one solution that preserves the physical bounds of the unknowns; furthermore, any sequence of approximate solutions to the discretized system of balance laws is shown to tend (up to a subsequence) to a weak solution of the continuous problem. In the inviscid case, the model should boil down, as the stiffness of reaction term increases, to a model for which a closed form of the solution of Riemann problems is available. Numerical tests are performed to show that this is indeed the case.The last part or the thesis is devoted to the discretization of a system of balance equations which models the low Mach number one-dimensional…

Advisors/Committee Members: Herbin, Raphaèle (thesis director), Latché, Jean-Claude (thesis director).

Subjects/Keywords: .; .; 510

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APA (6^th Edition):

Grapsas, D. (2017). Staggered fractional step numerical schemes for models for reactive flows : Schémas à mailles décalés pour des modèles d'écoulements compressible réactifs. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2017AIXM0566

Chicago Manual of Style (16^th Edition):

Grapsas, Dionysios. “Staggered fractional step numerical schemes for models for reactive flows : Schémas à mailles décalés pour des modèles d'écoulements compressible réactifs.” 2017. Doctoral Dissertation, Aix Marseille Université. Accessed April 17, 2021. http://www.theses.fr/2017AIXM0566.

MLA Handbook (7^th Edition):

Grapsas, Dionysios. “Staggered fractional step numerical schemes for models for reactive flows : Schémas à mailles décalés pour des modèles d'écoulements compressible réactifs.” 2017. Web. 17 Apr 2021.

Vancouver:

Grapsas D. Staggered fractional step numerical schemes for models for reactive flows : Schémas à mailles décalés pour des modèles d'écoulements compressible réactifs. [Internet] [Doctoral dissertation]. Aix Marseille Université 2017. [cited 2021 Apr 17]. Available from: http://www.theses.fr/2017AIXM0566.

Council of Science Editors:

Grapsas D. Staggered fractional step numerical schemes for models for reactive flows : Schémas à mailles décalés pour des modèles d'écoulements compressible réactifs. [Doctoral Dissertation]. Aix Marseille Université 2017. Available from: http://www.theses.fr/2017AIXM0566

University of Oxford

2. Lewin, Thomas. Modelling the impact of heterogeneity in tumour composition on the response to fractionated radiotherapy.

Degree: PhD, 2018, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:7c9ef972-2094-4f0d-a860-6a31fd75679e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791608

► Current protocols for delivering radiotherapy are based primarily on tumour stage and nodal and metastases (TNM) status, even though it is well known that tumours… (more)

▼ Current protocols for delivering radiotherapy are based primarily on tumour stage and nodal and metastases (TNM) status, even though it is well known that tumours and their microenvironments are highly heterogeneous. Mathematical models have the potential to inform protocol selection on a more patient-specific basis. However such applications require early prediction of tumour response and, thus, calibration of the model parameters from pre-treatment data which is typically limited to two CT scans - one at diagnosis and one at the treatment planning stage. In this thesis we aim to determine whether pre-treatment tumour volume data may be used to accurately predict tumour response to radiotherapy. We further aim to provide a mechanistic description of the different qualitative responses to radiotherapy observed in clinical data and the influence of intratumoural heterogeneity on these dynamics. Mathematical models for clinical applications typically contain few model parameters for ease of calibration with the sparse available data. Such models often take the form of single or multiple compartment ordinary differential equations (ODEs). We use parameter estimation and model selection techniques to perform both synthetic and clinical data studies and assess the predictive power of such models. We show that, while the models considered may be adequate in some cases, the range of qualitative dynamics exhibited by the clinical data extends beyond that which may be captured by these simple models. To address this discrepancy, we develop a suite of increasingly complex models that account for spatial heterogeneity in tumours, and use a range of methods to assess their validity and predictive power. In particular, we use a combination of numerical simulation and asymptotic analysis to investigate the dynamics of each model and the impact of increasing spatial heterogeneity on tumour response to radiotherapy. In vitro avascular tumour spheroids have a well-defined spatial structure, providing a simple geometry that is often exploited in tumour growth models. We extend one such model (Greenspan, 1972) to develop a new spatially-resolved model for tumour response to radiotherapy. Model simulations reveal a rapid transient increase in hypoxia upon regrowth of the tumour spheroid post-irradiation, a factor known to inhibit radiotherapy efficacy. We also investigate the response to different fractionation schedules and identify a tumour-specific relationship between inter-fraction time and dose per fraction to achieve cure. We further use the framework of multiphase mixtures to develop new models of both tumour growth and radiotherapy response that allow for the greater degree of heterogeneity typically observed in vivo. The multiphase models describe a wider range of spatial tumour compositions and consider mechanical interactions between different constituents of the tumour microenvironment. They reproduce the qualitative radiotherapy response dynamics observed in clinical data, including behaviours not captured by simpler…

Subjects/Keywords: 510

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APA (6^th Edition):

Lewin, T. (2018). Modelling the impact of heterogeneity in tumour composition on the response to fractionated radiotherapy. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:7c9ef972-2094-4f0d-a860-6a31fd75679e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791608

Chicago Manual of Style (16^th Edition):

Lewin, Thomas. “Modelling the impact of heterogeneity in tumour composition on the response to fractionated radiotherapy.” 2018. Doctoral Dissertation, University of Oxford. Accessed April 17, 2021. http://ora.ox.ac.uk/objects/uuid:7c9ef972-2094-4f0d-a860-6a31fd75679e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791608.

MLA Handbook (7^th Edition):

Lewin, Thomas. “Modelling the impact of heterogeneity in tumour composition on the response to fractionated radiotherapy.” 2018. Web. 17 Apr 2021.

Vancouver:

Lewin T. Modelling the impact of heterogeneity in tumour composition on the response to fractionated radiotherapy. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2021 Apr 17]. Available from: http://ora.ox.ac.uk/objects/uuid:7c9ef972-2094-4f0d-a860-6a31fd75679e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791608.

Council of Science Editors:

Lewin T. Modelling the impact of heterogeneity in tumour composition on the response to fractionated radiotherapy. [Doctoral Dissertation]. University of Oxford; 2018. Available from: http://ora.ox.ac.uk/objects/uuid:7c9ef972-2094-4f0d-a860-6a31fd75679e ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.791608

University of Exeter

3. Almuaddi, S. Control of spiral waves in reaction-diffusion systems using response function.

Degree: PhD, 2019, University of Exeter

URL: http://hdl.handle.net/10871/40100

► This thesis is motivated by the desire to understand spiral wave dynamics in reactiondiffusion systems with particular focus on the FitzHugh-Nagumo model. We attempt to… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Almuaddi, S. (2019). Control of spiral waves in reaction-diffusion systems using response function. (Doctoral Dissertation). University of Exeter. Retrieved from http://hdl.handle.net/10871/40100

Chicago Manual of Style (16^th Edition):

Almuaddi, S. “Control of spiral waves in reaction-diffusion systems using response function.” 2019. Doctoral Dissertation, University of Exeter. Accessed April 17, 2021. http://hdl.handle.net/10871/40100.

MLA Handbook (7^th Edition):

Almuaddi, S. “Control of spiral waves in reaction-diffusion systems using response function.” 2019. Web. 17 Apr 2021.

Vancouver:

Almuaddi S. Control of spiral waves in reaction-diffusion systems using response function. [Internet] [Doctoral dissertation]. University of Exeter; 2019. [cited 2021 Apr 17]. Available from: http://hdl.handle.net/10871/40100.

Council of Science Editors:

Almuaddi S. Control of spiral waves in reaction-diffusion systems using response function. [Doctoral Dissertation]. University of Exeter; 2019. Available from: http://hdl.handle.net/10871/40100

University of Sheffield

4. Edis, Sam. On arithmetic progressions and perfect powers.

Degree: PhD, 2019, University of Sheffield

URL: http://etheses.whiterose.ac.uk/25564/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798063

► In this thesis we will consider the problems that occur at the intersection of arithmetic progressions and perfect powers. In particular we will study the… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Edis, S. (2019). On arithmetic progressions and perfect powers. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/25564/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798063

Chicago Manual of Style (16^th Edition):

Edis, Sam. “On arithmetic progressions and perfect powers.” 2019. Doctoral Dissertation, University of Sheffield. Accessed April 17, 2021. http://etheses.whiterose.ac.uk/25564/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798063.

MLA Handbook (7^th Edition):

Edis, Sam. “On arithmetic progressions and perfect powers.” 2019. Web. 17 Apr 2021.

Vancouver:

Edis S. On arithmetic progressions and perfect powers. [Internet] [Doctoral dissertation]. University of Sheffield; 2019. [cited 2021 Apr 17]. Available from: http://etheses.whiterose.ac.uk/25564/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798063.

Council of Science Editors:

Edis S. On arithmetic progressions and perfect powers. [Doctoral Dissertation]. University of Sheffield; 2019. Available from: http://etheses.whiterose.ac.uk/25564/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798063

University of Sheffield

5. Yarrow, Mark. A journey down the rabbit hole : pondering preferential attachment models with location.

Degree: PhD, 2019, University of Sheffield

URL: http://etheses.whiterose.ac.uk/25764/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798091

► We investigate the use of stochastic approximation as a method of identifying conditions necessary to facilitate condensation and coexistence. We did this for a variety… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Yarrow, M. (2019). A journey down the rabbit hole : pondering preferential attachment models with location. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/25764/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798091

Chicago Manual of Style (16^th Edition):

Yarrow, Mark. “A journey down the rabbit hole : pondering preferential attachment models with location.” 2019. Doctoral Dissertation, University of Sheffield. Accessed April 17, 2021. http://etheses.whiterose.ac.uk/25764/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798091.

MLA Handbook (7^th Edition):

Yarrow, Mark. “A journey down the rabbit hole : pondering preferential attachment models with location.” 2019. Web. 17 Apr 2021.

Vancouver:

Yarrow M. A journey down the rabbit hole : pondering preferential attachment models with location. [Internet] [Doctoral dissertation]. University of Sheffield; 2019. [cited 2021 Apr 17]. Available from: http://etheses.whiterose.ac.uk/25764/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798091.

Council of Science Editors:

Yarrow M. A journey down the rabbit hole : pondering preferential attachment models with location. [Doctoral Dissertation]. University of Sheffield; 2019. Available from: http://etheses.whiterose.ac.uk/25764/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798091

6. Weiss, Ariel. On Galois representations associated to low weight Hilbert-Siegel modular forms.

Degree: PhD, 2019, University of Sheffield

URL: http://etheses.whiterose.ac.uk/25130/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789535

► Under the Langlands correspondence, where automorphic representations of GLₙ should correspond to n-dimensional Galois representations, 'cuspida' automorphic representations should correspond to 'irreducible' Galois representations. More… (more)

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Weiss, A. (2019). On Galois representations associated to low weight Hilbert-Siegel modular forms. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/25130/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789535

Chicago Manual of Style (16^th Edition):

Weiss, Ariel. “On Galois representations associated to low weight Hilbert-Siegel modular forms.” 2019. Doctoral Dissertation, University of Sheffield. Accessed April 17, 2021. http://etheses.whiterose.ac.uk/25130/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789535.

MLA Handbook (7^th Edition):

Weiss, Ariel. “On Galois representations associated to low weight Hilbert-Siegel modular forms.” 2019. Web. 17 Apr 2021.

Vancouver:

Weiss A. On Galois representations associated to low weight Hilbert-Siegel modular forms. [Internet] [Doctoral dissertation]. University of Sheffield; 2019. [cited 2021 Apr 17]. Available from: http://etheses.whiterose.ac.uk/25130/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789535.

Council of Science Editors:

Weiss A. On Galois representations associated to low weight Hilbert-Siegel modular forms. [Doctoral Dissertation]. University of Sheffield; 2019. Available from: http://etheses.whiterose.ac.uk/25130/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789535

University of Sheffield

7. Schembri, Ciaran. Modularity of abelian surfaces over imaginary quadratic fields.

Degree: PhD, 2019, University of Sheffield

URL: http://etheses.whiterose.ac.uk/24703/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798060

► Modular forms for GL(2) over an imaginary quadratic field K are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational… (more)

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Schembri, C. (2019). Modularity of abelian surfaces over imaginary quadratic fields. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/24703/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798060

Chicago Manual of Style (16^th Edition):

Schembri, Ciaran. “Modularity of abelian surfaces over imaginary quadratic fields.” 2019. Doctoral Dissertation, University of Sheffield. Accessed April 17, 2021. http://etheses.whiterose.ac.uk/24703/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798060.

MLA Handbook (7^th Edition):

Schembri, Ciaran. “Modularity of abelian surfaces over imaginary quadratic fields.” 2019. Web. 17 Apr 2021.

Vancouver:

Schembri C. Modularity of abelian surfaces over imaginary quadratic fields. [Internet] [Doctoral dissertation]. University of Sheffield; 2019. [cited 2021 Apr 17]. Available from: http://etheses.whiterose.ac.uk/24703/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798060.

Council of Science Editors:

Schembri C. Modularity of abelian surfaces over imaginary quadratic fields. [Doctoral Dissertation]. University of Sheffield; 2019. Available from: http://etheses.whiterose.ac.uk/24703/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.798060

University of Sheffield

8. Rendina, Angelo. Congruences of Saito-Kurokawa lifts and divisibility of degree-8 L-values.

Degree: PhD, 2019, University of Sheffield

URL: http://etheses.whiterose.ac.uk/25473/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.792069

► In this thesis, we study the arithmeticity of critical values of degree-8 tensor product L-functions attached to Siegel modular forms of genus 1 and 2.… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Rendina, A. (2019). Congruences of Saito-Kurokawa lifts and divisibility of degree-8 L-values. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/25473/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.792069

Chicago Manual of Style (16^th Edition):

Rendina, Angelo. “Congruences of Saito-Kurokawa lifts and divisibility of degree-8 L-values.” 2019. Doctoral Dissertation, University of Sheffield. Accessed April 17, 2021. http://etheses.whiterose.ac.uk/25473/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.792069.

MLA Handbook (7^th Edition):

Rendina, Angelo. “Congruences of Saito-Kurokawa lifts and divisibility of degree-8 L-values.” 2019. Web. 17 Apr 2021.

Vancouver:

Rendina A. Congruences of Saito-Kurokawa lifts and divisibility of degree-8 L-values. [Internet] [Doctoral dissertation]. University of Sheffield; 2019. [cited 2021 Apr 17]. Available from: http://etheses.whiterose.ac.uk/25473/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.792069.

Council of Science Editors:

Rendina A. Congruences of Saito-Kurokawa lifts and divisibility of degree-8 L-values. [Doctoral Dissertation]. University of Sheffield; 2019. Available from: http://etheses.whiterose.ac.uk/25473/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.792069

King's College London (University of London)

9. Facoetti, Davide. Ergodicity and localisation in mean-field quantum systems.

Degree: PhD, 2019, King's College London (University of London)

URL: https://kclpure.kcl.ac.uk/portal/en/theses/ergodicity-and-localisation-in-meanfield-quantum-systems(1d9d4aa5-21d0-47c5-a1b3-4c7f22b68fdd).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789273

► Recent years have seen a resurgence of interest in fundamental questions regarding the out-of-equilibrium behaviour of isolated quantum systems. Due to both new experimental techniques,… (more)

▼ Recent years have seen a resurgence of interest in fundamental questions regarding the out-of-equilibrium behaviour of isolated quantum systems. Due to both new experimental techniques, such as those involving cold atomic gases, and progress in the theoretical understanding of closed quantum systems, it is now possible to explore fundamental questions about thermalisation and the applicability of statistical mechanics. The interplay between disorder, interactions and quantum interference gives rise to interesting phenomena, such as many-body localisation (MBL), which has a key role in the non-equilibrium behaviour of such systems. Realistic models of disordered, interacting quantum systems are largely intractable analytically. Their numerical study is limited by the difficulty of simulating quantum systems with classical computers, making it challenging to separate genuine "thermodynamic" results from finite size effects. In this thesis we consider some more tractable mean- field models, as a starting point to investigate specific aspects of ergodicity and localisation transitions in many-body systems. The first part is devoted to the outstanding question of whether MBL systems undergo two separate ergodicity and localisation transitions when disorder strength is increased. The two transitions are separated by a putative "bad metal", nonergodic extended (NEE) phase, in which ergodicity is broken but the eigenstates are not exponentially localised. We show explicitly the existence of the NEE phase in a random matrix model, and characterise it using the local resolvent in an unusual scaling limit. In the second part we consider a spin glass model, in which quantum effects are introduced by a transverse magnetic field. A refined equilibrium phase diagram, going beyond the quasi-static approximation, is obtained with a numerically exact diagrammatic Monte Carlo approach. We discuss the difference between the ergodic, eigenstate and clustering transitions. Finally, we consider a quantum model that shares some of the peculiar low-temperature properties which have brought the Sachdev-Ye-Kitaev (SYK) model under the spotlight of the string theory community. In our model such properties are understood in terms of the glassy dynamics of a corresponding classical stochastic system.

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Facoetti, D. (2019). Ergodicity and localisation in mean-field quantum systems. (Doctoral Dissertation). King's College London (University of London). Retrieved from https://kclpure.kcl.ac.uk/portal/en/theses/ergodicity-and-localisation-in-meanfield-quantum-systems(1d9d4aa5-21d0-47c5-a1b3-4c7f22b68fdd).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789273

Chicago Manual of Style (16^th Edition):

Facoetti, Davide. “Ergodicity and localisation in mean-field quantum systems.” 2019. Doctoral Dissertation, King's College London (University of London). Accessed April 17, 2021. https://kclpure.kcl.ac.uk/portal/en/theses/ergodicity-and-localisation-in-meanfield-quantum-systems(1d9d4aa5-21d0-47c5-a1b3-4c7f22b68fdd).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789273.

MLA Handbook (7^th Edition):

Facoetti, Davide. “Ergodicity and localisation in mean-field quantum systems.” 2019. Web. 17 Apr 2021.

Vancouver:

Facoetti D. Ergodicity and localisation in mean-field quantum systems. [Internet] [Doctoral dissertation]. King's College London (University of London); 2019. [cited 2021 Apr 17]. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/ergodicity-and-localisation-in-meanfield-quantum-systems(1d9d4aa5-21d0-47c5-a1b3-4c7f22b68fdd).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789273.

Council of Science Editors:

Facoetti D. Ergodicity and localisation in mean-field quantum systems. [Doctoral Dissertation]. King's College London (University of London); 2019. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/ergodicity-and-localisation-in-meanfield-quantum-systems(1d9d4aa5-21d0-47c5-a1b3-4c7f22b68fdd).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789273

King's College London (University of London)

10. Heuer, Ben. Perfectoid geometry of p-adic modular forms.

Degree: PhD, 2019, King's College London (University of London)

URL: https://kclpure.kcl.ac.uk/portal/en/theses/perfectoid-geometry-of-padic-modular-forms(30325fef-65bb-4482-a813-e8fb23de2b96).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789304

► We prove a perfectoid tilting isomorphism that describes the Hecke module of over- convergent t-adic modular forms of Andreatta-Iovita-Pilloni at the boundary of weight space… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Heuer, B. (2019). Perfectoid geometry of p-adic modular forms. (Doctoral Dissertation). King's College London (University of London). Retrieved from https://kclpure.kcl.ac.uk/portal/en/theses/perfectoid-geometry-of-padic-modular-forms(30325fef-65bb-4482-a813-e8fb23de2b96).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789304

Chicago Manual of Style (16^th Edition):

Heuer, Ben. “Perfectoid geometry of p-adic modular forms.” 2019. Doctoral Dissertation, King's College London (University of London). Accessed April 17, 2021. https://kclpure.kcl.ac.uk/portal/en/theses/perfectoid-geometry-of-padic-modular-forms(30325fef-65bb-4482-a813-e8fb23de2b96).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789304.

MLA Handbook (7^th Edition):

Heuer, Ben. “Perfectoid geometry of p-adic modular forms.” 2019. Web. 17 Apr 2021.

Vancouver:

Heuer B. Perfectoid geometry of p-adic modular forms. [Internet] [Doctoral dissertation]. King's College London (University of London); 2019. [cited 2021 Apr 17]. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/perfectoid-geometry-of-padic-modular-forms(30325fef-65bb-4482-a813-e8fb23de2b96).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789304.

Council of Science Editors:

Heuer B. Perfectoid geometry of p-adic modular forms. [Doctoral Dissertation]. King's College London (University of London); 2019. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/perfectoid-geometry-of-padic-modular-forms(30325fef-65bb-4482-a813-e8fb23de2b96).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789304

11. Pettit, Michaella Louise. E theory : its algebra, gauge fixing, and 7D equations of motion.

Degree: PhD, 2019, King's College London (University of London)

URL: https://kclpure.kcl.ac.uk/portal/en/theses/e-theory(6d30c9d8-9803-49eb-bae9-1576449aec2d).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789191

► It has been proposed that all strings and branes are contained in the non-linear realisation of the Kac-Moody algebra E₁₁ with the semi-direct product of… (more)

▼ It has been proposed that all strings and branes are contained in the non-linear realisation of the Kac-Moody algebra E₁₁ with the semi-direct product of its fundamental representation l₁, denoted E₁₁ ⊗_sl₁. In the process of building the non-linear realisation, the dynamics of strings and branes are naturally invariant under symmetries which are determined by the relevant decomposition of the E₁₁ algebra. At low levels, these dynamics are exactly those of D dimensional maximal supergravity, constructed from the subgroup GL(D) ⊗E_11-D, with the fields and coordinates of the theory appearing as parameters of the generators of the algebra. In this thesis, we first construct relevant decompositions of the E₁₁ ⊗_sl₁ algebra. We begin by extending previous calculations of the algebra of the 11D decomposition up to levels 5 and 6 in the adjoint representation. We then calculate the algebra of the 7D decomposition in the adjoint representation, vector representation, and Cartan involution invariant subalgebra up to level 5. The final algebra that we calculate is the 10 dimensional IIB Cartan involution invariant subalgebra up to level 4. We then build a tangent space metric in the 11D, 5D, and 4D decompositions of the E₁₁ algebra, and additionally for the A₁⁺⁺⁺ algebra, which leads to a description of 4 dimensional gravity. These tangent space metrics are then used to build a set of gaugefixing conditions which allow gauge symmetries to be fixed in an E₁₁ covariant way. The final part of the thesis constructs the non-linear realisation in the 7 dimensional decomposition of E₁₁ at low levels, using the algebra derived in an earlier chapter. This is then used to find a set of dynamical equations, which, when truncated, agree exactly with the equations of motion for the graviton, the scalar, the one-form, and the two-form in 7D maximal supergravity. Finally, we derive the duality relations of the scalar and the graviton with their corresponding dual fields, from the duality relations of the 1-form and 2-form found in the previous section.

Subjects/Keywords: 510

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APA (6^th Edition):

Pettit, M. L. (2019). E theory : its algebra, gauge fixing, and 7D equations of motion. (Doctoral Dissertation). King's College London (University of London). Retrieved from https://kclpure.kcl.ac.uk/portal/en/theses/e-theory(6d30c9d8-9803-49eb-bae9-1576449aec2d).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789191

Chicago Manual of Style (16^th Edition):

Pettit, Michaella Louise. “E theory : its algebra, gauge fixing, and 7D equations of motion.” 2019. Doctoral Dissertation, King's College London (University of London). Accessed April 17, 2021. https://kclpure.kcl.ac.uk/portal/en/theses/e-theory(6d30c9d8-9803-49eb-bae9-1576449aec2d).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789191.

MLA Handbook (7^th Edition):

Pettit, Michaella Louise. “E theory : its algebra, gauge fixing, and 7D equations of motion.” 2019. Web. 17 Apr 2021.

Vancouver:

Pettit ML. E theory : its algebra, gauge fixing, and 7D equations of motion. [Internet] [Doctoral dissertation]. King's College London (University of London); 2019. [cited 2021 Apr 17]. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/e-theory(6d30c9d8-9803-49eb-bae9-1576449aec2d).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789191.

Council of Science Editors:

Pettit ML. E theory : its algebra, gauge fixing, and 7D equations of motion. [Doctoral Dissertation]. King's College London (University of London); 2019. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/e-theory(6d30c9d8-9803-49eb-bae9-1576449aec2d).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789191

King's College London (University of London)

12. Steinmetz, Misja Frederik Alban. Explicit Serre weights for two-dimensional Galois representations.

Degree: PhD, 2020, King's College London (University of London)

URL: https://kclpure.kcl.ac.uk/portal/en/theses/explicit-serre-weights-for-twodimensional-galois-representations(064531b0-7481-4432-b15a-9ca29b4cf56c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.797838

► Let F be a totally real field and p a prime number. Given a Galois representation ρ : G_F → GL₂(Fp), we have precise conjectures… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Steinmetz, M. F. A. (2020). Explicit Serre weights for two-dimensional Galois representations. (Doctoral Dissertation). King's College London (University of London). Retrieved from https://kclpure.kcl.ac.uk/portal/en/theses/explicit-serre-weights-for-twodimensional-galois-representations(064531b0-7481-4432-b15a-9ca29b4cf56c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.797838

Chicago Manual of Style (16^th Edition):

Steinmetz, Misja Frederik Alban. “Explicit Serre weights for two-dimensional Galois representations.” 2020. Doctoral Dissertation, King's College London (University of London). Accessed April 17, 2021. https://kclpure.kcl.ac.uk/portal/en/theses/explicit-serre-weights-for-twodimensional-galois-representations(064531b0-7481-4432-b15a-9ca29b4cf56c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.797838.

MLA Handbook (7^th Edition):

Steinmetz, Misja Frederik Alban. “Explicit Serre weights for two-dimensional Galois representations.” 2020. Web. 17 Apr 2021.

Vancouver:

Steinmetz MFA. Explicit Serre weights for two-dimensional Galois representations. [Internet] [Doctoral dissertation]. King's College London (University of London); 2020. [cited 2021 Apr 17]. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/explicit-serre-weights-for-twodimensional-galois-representations(064531b0-7481-4432-b15a-9ca29b4cf56c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.797838.

Council of Science Editors:

Steinmetz MFA. Explicit Serre weights for two-dimensional Galois representations. [Doctoral Dissertation]. King's College London (University of London); 2020. Available from: https://kclpure.kcl.ac.uk/portal/en/theses/explicit-serre-weights-for-twodimensional-galois-representations(064531b0-7481-4432-b15a-9ca29b4cf56c).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.797838

University College London (University of London)

13. Lambert, Anna. Mathematical analysis for two cell culture problems : population balance frameworks & glycoprotein production.

Degree: PhD, 2019, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/10077211/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790880

► Genetically engineered cells are grown in bioreactors, and produce a wide range of important products, including many new medicines. Mathematical modelling of cell populations can… (more)

▼ Genetically engineered cells are grown in bioreactors, and produce a wide range of important products, including many new medicines. Mathematical modelling of cell populations can increase our understanding of their behaviour, potentially leading to increased manufacturing efficiency. This thesis considers two problems in cell culture modelling; population balance frameworks and glycoprotein production, both of which use analytical techniques to provide insight. Population balance equations provide a mathematical framework for the modelling of heterogeneous cells. They have few analytical solutions and multi-dimensional models are poorly understood. A novel analytical method for the solution of one dimensional models is developed in this thesis by converting the governing equation to an ordinary differential equation with delay. This provides insight into how the growth and division rate functions affect the shape of the cell distribution. In the two-dimensional case, a thorough investigation is presented on the shape of the cell distribution, given different growth rate functions and equal/unequal cell division. These interactions are complex, with several cases counterintuitively leading to biologically implausible solutions. A wide family of cases show limited heterogeneity across multiple dimensions, in line with results reported in the literature. The study highlights that careful consideration should be given to the use of multi-dimensional cell population balance models. Many new medicines produced in cell culture are glycoproteins: a protein with a large complex glycan molecule attached. These glycans are critical to medicine quality, but there is significant heterogeneity between the molecules. A novel ordinary differential equation model of glycoprotein production within cell culture is presented, which consists of two coupled submodels. The bioreactor submodel describes behaviour at the population and cell level, and the glycosylation submodel describes the molecular basis for glycosylation. Analytical solutions are found for both. Combining the two models shows that the quality of glycoproteins can vary through time depending on the substrate configuration.

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lambert, A. (2019). Mathematical analysis for two cell culture problems : population balance frameworks & glycoprotein production. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/10077211/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790880

Chicago Manual of Style (16^th Edition):

Lambert, Anna. “Mathematical analysis for two cell culture problems : population balance frameworks & glycoprotein production.” 2019. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/10077211/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790880.

MLA Handbook (7^th Edition):

Lambert, Anna. “Mathematical analysis for two cell culture problems : population balance frameworks & glycoprotein production.” 2019. Web. 17 Apr 2021.

Vancouver:

Lambert A. Mathematical analysis for two cell culture problems : population balance frameworks & glycoprotein production. [Internet] [Doctoral dissertation]. University College London (University of London); 2019. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/10077211/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790880.

Council of Science Editors:

Lambert A. Mathematical analysis for two cell culture problems : population balance frameworks & glycoprotein production. [Doctoral Dissertation]. University College London (University of London); 2019. Available from: https://discovery.ucl.ac.uk/id/eprint/10077211/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790880

University College London (University of London)

14. Torricelli, L. Modeling of volatility-linked financial products.

Degree: PhD, 2016, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1476794/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790186

► This thesis is the collation of four papers, adapted from their original versions as to form here four distinct chapters. In the first chapter we… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Torricelli, L. (2016). Modeling of volatility-linked financial products. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1476794/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790186

Chicago Manual of Style (16^th Edition):

Torricelli, L. “Modeling of volatility-linked financial products.” 2016. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1476794/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790186.

MLA Handbook (7^th Edition):

Torricelli, L. “Modeling of volatility-linked financial products.” 2016. Web. 17 Apr 2021.

Vancouver:

Torricelli L. Modeling of volatility-linked financial products. [Internet] [Doctoral dissertation]. University College London (University of London); 2016. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1476794/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790186.

Council of Science Editors:

Torricelli L. Modeling of volatility-linked financial products. [Doctoral Dissertation]. University College London (University of London); 2016. Available from: https://discovery.ucl.ac.uk/id/eprint/1476794/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790186

University College London (University of London)

15. Boiveau, T. B. V. Penalty-free Nitsche method for interface problems in computational mechanics.

Degree: PhD, 2016, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1503355/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790348

► Nitsche's method is a penalty-based method to enforce weakly the boundary conditions in the finite element method. In this thesis, we consider a penalty-free version… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Boiveau, T. B. V. (2016). Penalty-free Nitsche method for interface problems in computational mechanics. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1503355/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790348

Chicago Manual of Style (16^th Edition):

Boiveau, T B V. “Penalty-free Nitsche method for interface problems in computational mechanics.” 2016. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1503355/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790348.

MLA Handbook (7^th Edition):

Boiveau, T B V. “Penalty-free Nitsche method for interface problems in computational mechanics.” 2016. Web. 17 Apr 2021.

Vancouver:

Boiveau TBV. Penalty-free Nitsche method for interface problems in computational mechanics. [Internet] [Doctoral dissertation]. University College London (University of London); 2016. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1503355/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790348.

Council of Science Editors:

Boiveau TBV. Penalty-free Nitsche method for interface problems in computational mechanics. [Doctoral Dissertation]. University College London (University of London); 2016. Available from: https://discovery.ucl.ac.uk/id/eprint/1503355/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790348

University College London (University of London)

16. Laaksonen, N. P. J. Quantum limits, counting and Landau-type formulae in hyperbolic space.

Degree: PhD, 2016, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1474273/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790105

► In this thesis we explore a variety of topics in analytic number theory and automorphic forms. In the classical context, we look at the value… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Laaksonen, N. P. J. (2016). Quantum limits, counting and Landau-type formulae in hyperbolic space. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1474273/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790105

Chicago Manual of Style (16^th Edition):

Laaksonen, N P J. “Quantum limits, counting and Landau-type formulae in hyperbolic space.” 2016. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1474273/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790105.

MLA Handbook (7^th Edition):

Laaksonen, N P J. “Quantum limits, counting and Landau-type formulae in hyperbolic space.” 2016. Web. 17 Apr 2021.

Vancouver:

Laaksonen NPJ. Quantum limits, counting and Landau-type formulae in hyperbolic space. [Internet] [Doctoral dissertation]. University College London (University of London); 2016. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1474273/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790105.

Council of Science Editors:

Laaksonen NPJ. Quantum limits, counting and Landau-type formulae in hyperbolic space. [Doctoral Dissertation]. University College London (University of London); 2016. Available from: https://discovery.ucl.ac.uk/id/eprint/1474273/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790105

University College London (University of London)

17. Hashimoto, Y. Some results on stability and canonical metrics in Kähler geometry.

Degree: PhD, 2015, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1470406/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789848

► In this thesis, we prove various results on canonical metrics in Kähler geometry, such as extremal metrics or constant scalar curvature Kähler (cscK) metrics, and… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Hashimoto, Y. (2015). Some results on stability and canonical metrics in Kähler geometry. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1470406/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789848

Chicago Manual of Style (16^th Edition):

Hashimoto, Y. “Some results on stability and canonical metrics in Kähler geometry.” 2015. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1470406/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789848.

MLA Handbook (7^th Edition):

Hashimoto, Y. “Some results on stability and canonical metrics in Kähler geometry.” 2015. Web. 17 Apr 2021.

Vancouver:

Hashimoto Y. Some results on stability and canonical metrics in Kähler geometry. [Internet] [Doctoral dissertation]. University College London (University of London); 2015. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1470406/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789848.

Council of Science Editors:

Hashimoto Y. Some results on stability and canonical metrics in Kähler geometry. [Doctoral Dissertation]. University College London (University of London); 2015. Available from: https://discovery.ucl.ac.uk/id/eprint/1470406/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789848

University College London (University of London)

18. Bartlett, T. E. Network models of stochastic processes in cancer.

Degree: PhD, 2015, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1471225/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789897

► Complex systems which can be modelled as networks are ubiquitous. Well-known examples include social and economic networks, as well as many examples in cell biology… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Bartlett, T. E. (2015). Network models of stochastic processes in cancer. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1471225/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789897

Chicago Manual of Style (16^th Edition):

Bartlett, T E. “Network models of stochastic processes in cancer.” 2015. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1471225/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789897.

MLA Handbook (7^th Edition):

Bartlett, T E. “Network models of stochastic processes in cancer.” 2015. Web. 17 Apr 2021.

Vancouver:

Bartlett TE. Network models of stochastic processes in cancer. [Internet] [Doctoral dissertation]. University College London (University of London); 2015. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1471225/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789897.

Council of Science Editors:

Bartlett TE. Network models of stochastic processes in cancer. [Doctoral Dissertation]. University College London (University of London); 2015. Available from: https://discovery.ucl.ac.uk/id/eprint/1471225/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789897

University College London (University of London)

19. Mohd. Ramli, N. H. B. Stochastic trajectory modelling of atmospheric dispersion.

Degree: PhD, 2016, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1531940/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790558

► The stochastic trajectory-based (Lagrangian) approach has gained increasing importance and sophistication in atmospheric transport and dispersion modelling over the last few decades. State-of-the-art Lagrangian particle… (more)

▼ The stochastic trajectory-based (Lagrangian) approach has gained increasing importance and sophistication in atmospheric transport and dispersion modelling over the last few decades. State-of-the-art Lagrangian particle dispersion model (LPDMs) are used to compute trajectories of a large number of 'marked' particles and numerically simulate the dispersion of a pollutant (passive tracer) in the turbulent atmosphere. In this thesis, we mainly investigate the stochastic formulation and behaviour of LPDMs in the context of the turbulent atmospheric boundary layer (ABL). A random flight model (RFM) is a type of LPDM that describes the paths of particles of an air pollutant in a turbulent flow, given a statistical knowledge of the random velocity field. Operational RFMs such as FLEXPART have not taken advantage of modern developments of numerical methods for stochastic differential equations. Chapter 2 of this thesis aims to determine whether current numerical schemes used in operational atmospheric dispersion modelling can be improved. Several commonly used numerical schemes are investigated in a simple one-dimensional dispersion model describing the vertical turbulence in the ABL. Eulerian Fokker-Planck equation (FPE) solutions with the required level of accuracy are used to validate the performance of the RFM numerical schemes. The results allow for optimal time-step selection and recommendations to be made for use in operational models. RFMs are known to have a finite Lagrangian decorrelation time. Another class of LPDMs are the random displacement models (RDMs), which are essentially the zero decorrelation time limit of the RFMs. In Chapter 3, the problem of shear dispersion in the ABL is revisited, with the aim to improve understanding of how and why the behaviour of RFMs can differ to the RDMs. First, the effective horizontal diffusivity is examined for a tracer in the long-time dispersion in the RFM. Second, with `poison gas release' problems in mind, a large-deviation approach is used to understand in greater detail the behaviour of the concentration in the tails of the distribution. Results are verified by solving the LPDM equations numerically for a large ensemble of particles. Chapter 4 discusses methods of kernel density estimation for the optimal construction of particle concentration fields from the trajectory distributions. We demonstrate these methods on a two-dimensional advection-diffusion model (equivalent to the RDM) in a chaotic advection flow. Some well-known techniques of bandwidth selection are briefly discussed and a new approach in constructing a kernel density estimator is developed.

Subjects/Keywords: 510

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APA (6^th Edition):

Mohd. Ramli, N. H. B. (2016). Stochastic trajectory modelling of atmospheric dispersion. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1531940/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790558

Chicago Manual of Style (16^th Edition):

Mohd. Ramli, N H B. “Stochastic trajectory modelling of atmospheric dispersion.” 2016. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1531940/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790558.

MLA Handbook (7^th Edition):

Mohd. Ramli, N H B. “Stochastic trajectory modelling of atmospheric dispersion.” 2016. Web. 17 Apr 2021.

Vancouver:

Mohd. Ramli NHB. Stochastic trajectory modelling of atmospheric dispersion. [Internet] [Doctoral dissertation]. University College London (University of London); 2016. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1531940/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790558.

Council of Science Editors:

Mohd. Ramli NHB. Stochastic trajectory modelling of atmospheric dispersion. [Doctoral Dissertation]. University College London (University of London); 2016. Available from: https://discovery.ucl.ac.uk/id/eprint/1531940/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790558

University College London (University of London)

20. Chatzakos, D. Lattice point problems in the hyperbolic plane.

Degree: PhD, 2016, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1521768/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790460

In this thesis we investigate two different lattice point problems in the hyperbolic plane, the classical hyperbolic lattice point problem and the hyperbolic lattice point problem in conjugacy classes. In order to study these problems we use tools from the harmonic analysis on the hyperbolic plane H.

Subjects/Keywords: 510

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APA (6^th Edition):

Chatzakos, D. (2016). Lattice point problems in the hyperbolic plane. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1521768/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790460

Chicago Manual of Style (16^th Edition):

Chatzakos, D. “Lattice point problems in the hyperbolic plane.” 2016. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1521768/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790460.

MLA Handbook (7^th Edition):

Chatzakos, D. “Lattice point problems in the hyperbolic plane.” 2016. Web. 17 Apr 2021.

Vancouver:

Chatzakos D. Lattice point problems in the hyperbolic plane. [Internet] [Doctoral dissertation]. University College London (University of London); 2016. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1521768/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790460.

Council of Science Editors:

Chatzakos D. Lattice point problems in the hyperbolic plane. [Doctoral Dissertation]. University College London (University of London); 2016. Available from: https://discovery.ucl.ac.uk/id/eprint/1521768/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790460

University College London (University of London)

21. Luu, T. Fast and accurate parallel computation of quantile functions for random number generation.

Degree: PhD, 2016, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1482128/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790241

► The fast and accurate computation of quantile functions (the inverse of cumulative distribution functions) is very desirable for generating random variates from non-uniform probability distributions.… (more)

▼ The fast and accurate computation of quantile functions (the inverse of cumulative distribution functions) is very desirable for generating random variates from non-uniform probability distributions. This is because the quantile function of a distribution monotonically maps uniform variates to variates of the said distribution. This simple fact is the basis of the inversion method for generating non-uniform random numbers. The inversion method enjoys many significant advantages, which is why it is regarded as the best choice for random number generation. Quantile functions preserve the underlying properties of the uniform variates, which is beneficial for a number of applications, especially in modern computational finance. For example, copula and quasi-Monte Carlo methods are significantly easier to use with inversion. Inversion is also well suited to variance reduction techniques. However, for a number of key distributions, existing methods for the computational of their quantile functions are too slow in practice. The methods are also unsuited to execution on parallel architectures such as GPUs and FPGAs. These parallel architectures have become very popular, because they allow simulations to be sped up and enlarged. The original contribution of this thesis is a collection of new and practical numerical algorithms for the normal, gamma, non-central χ2 and skew-normal quantile functions. The algorithms were developed with efficient parallel computation in mind. Quantile mechanics-the differential approach to quantile functions-was used with inventive changes of variables and numerical methods to create the algorithms. The algorithms are faster or more accurate than the current state of the art on parallel architectures. The accuracy of GPU implementations of the algorithms have been benchmarked against independent CPU implementations. The results indicate that the quantile mechanics approach is a viable and powerful technique for developing quantile function approximations and algorithms.

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Luu, T. (2016). Fast and accurate parallel computation of quantile functions for random number generation. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1482128/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790241

Chicago Manual of Style (16^th Edition):

Luu, T. “Fast and accurate parallel computation of quantile functions for random number generation.” 2016. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1482128/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790241.

MLA Handbook (7^th Edition):

Luu, T. “Fast and accurate parallel computation of quantile functions for random number generation.” 2016. Web. 17 Apr 2021.

Vancouver:

Luu T. Fast and accurate parallel computation of quantile functions for random number generation. [Internet] [Doctoral dissertation]. University College London (University of London); 2016. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1482128/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790241.

Council of Science Editors:

Luu T. Fast and accurate parallel computation of quantile functions for random number generation. [Doctoral Dissertation]. University College London (University of London); 2016. Available from: https://discovery.ucl.ac.uk/id/eprint/1482128/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790241

University College London (University of London)

22. Wray, C. M. Complex systems models of financial and systemic risk.

Degree: PhD, 2015, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1472883/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790009

► The primary purpose of this thesis is to develop mathematical models and tools that aid the understanding of financial systemic risk, by analysing and applying… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Wray, C. M. (2015). Complex systems models of financial and systemic risk. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1472883/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790009

Chicago Manual of Style (16^th Edition):

Wray, C M. “Complex systems models of financial and systemic risk.” 2015. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1472883/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790009.

MLA Handbook (7^th Edition):

Wray, C M. “Complex systems models of financial and systemic risk.” 2015. Web. 17 Apr 2021.

Vancouver:

Wray CM. Complex systems models of financial and systemic risk. [Internet] [Doctoral dissertation]. University College London (University of London); 2015. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1472883/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790009.

Council of Science Editors:

Wray CM. Complex systems models of financial and systemic risk. [Doctoral Dissertation]. University College London (University of London); 2015. Available from: https://discovery.ucl.ac.uk/id/eprint/1472883/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.790009

University College London (University of London)

23. Gerken, J. L. An objective analysis of alternative risk-to-reward ratios.

Degree: PhD, 2015, University College London (University of London)

URL: https://discovery.ucl.ac.uk/id/eprint/1472261/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789982

► This thesis is devoted to the task of investigating the merits of employing a generalised reward-to-risk ratio for the dual purpose of ranking assets and… (more)

▼ This thesis is devoted to the task of investigating the merits of employing a generalised reward-to-risk ratio for the dual purpose of ranking assets and forming optimal portfolios. In quantitative portfolio optimisation and risk management, the optimal allocation of assets often relies on traditional and well-established measures including the Sharpe ratio. Despite their frequently-documented drawbacks, these quantitative tools continue to be relied on. This is partly due to familiarity and ease of use. Another reason stems from the empirical evidence that alternative and more complex measures often produce results highly correlated with those based on their standard counterparts. This thesis presents an objective analysis of various risk-to-reward measures, for the purpose of portfolio optimisation, which are flexible enough to represent asymmetry in risk and return preferences. In particular, we regard the one-sided variability ratio (Farinelli and Tibiletti (2002)), ϕ(b; p; q), as an intuitive tool to be used in an optimal allocation model on account of its flexibility and ability to account for any distributional model. Focusing on two parameterisations of ϕ(b; p; q) (Omega = ϕ(b; 1; 1) and Sortino ratio = ϕ(b; 1; 2)), we show how these ratios can be analytically reduced to functions of the Sharpe ratio based on Student t returns. This sheds unfavourable light on such alternative and supposedly superior measures and verifies what practitioners commonly observe: that several theoretically advocated ratios replicate the same, or near identical, outcomes as the Sharpe ratio. Analogously, Eling and Schuhmacher (2012) provide further support for this hypothesis, conditional on the location-scale property being satisfied. Relaxing this distributional assumption, however, we cannot claim that ratios including Omega and Sortino do not produce substantially different results to the Sharpe ratio. In an empirical setting, it is questionable to suppose that return distributions satisfy the location-scale property. We consider anisotropic bivariate distributions proposed by Shaw and Lee (2008) to facilitate the simulation of situations where alternative measures produce different results in terms of asset rankings and dissimilar optimal asset weights. In light of this, we argue that it is critical to take an objective approach to constructing a portfolio optimisation model from modelling the underlying data to selecting the relevant risk and performance measures.

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gerken, J. L. (2015). An objective analysis of alternative risk-to-reward ratios. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1472261/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789982

Chicago Manual of Style (16^th Edition):

Gerken, J L. “An objective analysis of alternative risk-to-reward ratios.” 2015. Doctoral Dissertation, University College London (University of London). Accessed April 17, 2021. https://discovery.ucl.ac.uk/id/eprint/1472261/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789982.

MLA Handbook (7^th Edition):

Gerken, J L. “An objective analysis of alternative risk-to-reward ratios.” 2015. Web. 17 Apr 2021.

Vancouver:

Gerken JL. An objective analysis of alternative risk-to-reward ratios. [Internet] [Doctoral dissertation]. University College London (University of London); 2015. [cited 2021 Apr 17]. Available from: https://discovery.ucl.ac.uk/id/eprint/1472261/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789982.

Council of Science Editors:

Gerken JL. An objective analysis of alternative risk-to-reward ratios. [Doctoral Dissertation]. University College London (University of London); 2015. Available from: https://discovery.ucl.ac.uk/id/eprint/1472261/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.789982

University of Bristol

24. Biggs, Kirsti D. On additive problems involving shifted integers and ellipsephic sets.

Degree: PhD, 2019, University of Bristol

URL: http://hdl.handle.net/1983/0869179e-7873-49d3-9fc6-9456bde2830c

► In this thesis, we present a series of results concerning the number of solutions to equations and inequalities involving sums of perfect powers. In order… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Biggs, K. D. (2019). On additive problems involving shifted integers and ellipsephic sets. (Doctoral Dissertation). University of Bristol. Retrieved from http://hdl.handle.net/1983/0869179e-7873-49d3-9fc6-9456bde2830c

Chicago Manual of Style (16^th Edition):

Biggs, Kirsti D. “On additive problems involving shifted integers and ellipsephic sets.” 2019. Doctoral Dissertation, University of Bristol. Accessed April 17, 2021. http://hdl.handle.net/1983/0869179e-7873-49d3-9fc6-9456bde2830c.

MLA Handbook (7^th Edition):

Biggs, Kirsti D. “On additive problems involving shifted integers and ellipsephic sets.” 2019. Web. 17 Apr 2021.

Vancouver:

Biggs KD. On additive problems involving shifted integers and ellipsephic sets. [Internet] [Doctoral dissertation]. University of Bristol; 2019. [cited 2021 Apr 17]. Available from: http://hdl.handle.net/1983/0869179e-7873-49d3-9fc6-9456bde2830c.

Council of Science Editors:

Biggs KD. On additive problems involving shifted integers and ellipsephic sets. [Doctoral Dissertation]. University of Bristol; 2019. Available from: http://hdl.handle.net/1983/0869179e-7873-49d3-9fc6-9456bde2830c

Aberystwyth University

25. Zaccagnino, Francesca. Numerical simulation of surfactant motion in flowing foams and application to biological tissues.

Degree: PhD, 2019, Aberystwyth University

URL: http://hdl.handle.net/2160/1d660273-389c-4a95-be08-c3b79e330015

► We present a numerical model to study the rheology of two-dimensional dry foams. In a foam flowing at high velocity, the tangential component of the… (more)

▼ We present a numerical model to study the rheology of two-dimensional dry foams. In a foam flowing at high velocity, the tangential component of the velocity associated with the gradient of surfactant concentration is not negligible. We develop a dynamical model to investigate the influence of viscoelastic parameters on the film evolution. Particularly, we consider the surfactant transport and the consequent surface tension variation along each film. Moreover, experiments on a foam between two parallel plates suggest that the diffusion of curvature along the film controlled by external friction can not be neglected. Hence, we merge our surfactant transport (ST) model with the two-dimensional Viscous Froth (VF) model [45]. The VF+ST model is validated by fitting experimental data for the evolution of the length of a film after a topological rearrangement (T1). Extending the VF model, which allows us to estimate the drag coefficient, our VF+ST model predicts two additional parameters, the Gibbs elasticity and the surface viscosity. With the VF+ST model we can fit experimental data for both foam containing anionic surfactants or proteins [74]. Furthermore, we apply the VF+ST model to predict rheological parameters of a flowing two-dimensional dry foam. We implement situations in which hexagonal and disordered foams subjected to simple shear or oscillating strain. We highlight how the viscoelastic parameters of our model affect the distribution of topological rearrangements in the foam. Additionally, we calculate the shear stress which offer a qualitative description of the transition of the foam from a solid-like to a liquid-like behaviour. Hence, starting from the stress-strain curves at different shear rates we predict the elastic shear modulus and the yield stress of the foam. In case of oscillating strain we investigate how the foam behaviour changes when varying the frequency or the amplitude of the applied strain and we calculate the storage and loss moduli. Overall, we analyse the effect of the viscoelastic parameters of our model on the rheological properties of the foam. Finally, the model is applied to investigate the morphology of biological tissues. Well-known analogies between fluids and biological tissues make possible the application of our model to simulate experiments presented by Bonnet et al. [6]. They carried out an annular ablation on Drosophila pupa dorsal thorax epithelium. In agreement with the experimental results we find that after cutting the cell-cell junctions and relaxing the tissue to its configuration of mechanical equilibrium, the anisotropy in the tissue increases with the age of the Drosophila pupa. Also in this case we investigate the effect of our viscoelastic parameters on the tissue. We propose our model as a tool for further investigations on tissue morphology.

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zaccagnino, F. (2019). Numerical simulation of surfactant motion in flowing foams and application to biological tissues. (Doctoral Dissertation). Aberystwyth University. Retrieved from http://hdl.handle.net/2160/1d660273-389c-4a95-be08-c3b79e330015

Chicago Manual of Style (16^th Edition):

Zaccagnino, Francesca. “Numerical simulation of surfactant motion in flowing foams and application to biological tissues.” 2019. Doctoral Dissertation, Aberystwyth University. Accessed April 17, 2021. http://hdl.handle.net/2160/1d660273-389c-4a95-be08-c3b79e330015.

MLA Handbook (7^th Edition):

Zaccagnino, Francesca. “Numerical simulation of surfactant motion in flowing foams and application to biological tissues.” 2019. Web. 17 Apr 2021.

Vancouver:

Zaccagnino F. Numerical simulation of surfactant motion in flowing foams and application to biological tissues. [Internet] [Doctoral dissertation]. Aberystwyth University; 2019. [cited 2021 Apr 17]. Available from: http://hdl.handle.net/2160/1d660273-389c-4a95-be08-c3b79e330015.

Council of Science Editors:

Zaccagnino F. Numerical simulation of surfactant motion in flowing foams and application to biological tissues. [Doctoral Dissertation]. Aberystwyth University; 2019. Available from: http://hdl.handle.net/2160/1d660273-389c-4a95-be08-c3b79e330015

Aberystwyth University

26. Molinarolo, Riccardo. Nonlinear transmission problems for the Laplace operator : a functional analytic approach.

Degree: PhD, 2019, Aberystwyth University

URL: http://hdl.handle.net/2160/3e44683b-f1d5-4f60-bdaf-5dde5234d042

► This dissertation is devoted to the study of two nonlinear nonautonomous transmission boundary value problems for the Laplace operator in perturbed domains. From a geometrical… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Molinarolo, R. (2019). Nonlinear transmission problems for the Laplace operator : a functional analytic approach. (Doctoral Dissertation). Aberystwyth University. Retrieved from http://hdl.handle.net/2160/3e44683b-f1d5-4f60-bdaf-5dde5234d042

Chicago Manual of Style (16^th Edition):

Molinarolo, Riccardo. “Nonlinear transmission problems for the Laplace operator : a functional analytic approach.” 2019. Doctoral Dissertation, Aberystwyth University. Accessed April 17, 2021. http://hdl.handle.net/2160/3e44683b-f1d5-4f60-bdaf-5dde5234d042.

MLA Handbook (7^th Edition):

Molinarolo, Riccardo. “Nonlinear transmission problems for the Laplace operator : a functional analytic approach.” 2019. Web. 17 Apr 2021.

Vancouver:

Molinarolo R. Nonlinear transmission problems for the Laplace operator : a functional analytic approach. [Internet] [Doctoral dissertation]. Aberystwyth University; 2019. [cited 2021 Apr 17]. Available from: http://hdl.handle.net/2160/3e44683b-f1d5-4f60-bdaf-5dde5234d042.

Council of Science Editors:

Molinarolo R. Nonlinear transmission problems for the Laplace operator : a functional analytic approach. [Doctoral Dissertation]. Aberystwyth University; 2019. Available from: http://hdl.handle.net/2160/3e44683b-f1d5-4f60-bdaf-5dde5234d042

27. Christof, Constantin. A priori Fehlerabschätzungen für die FE-Diskretisierung klassischer Hindernisprobleme.

Degree: 2015, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-16454

► Wie wir in dieser Arbeit gesehen haben, verändern sich die Approximationseigenschaften der Näherungslösungen uh 2 V 0 h ( ), die man mit der Methode… (more)

▼ Wie wir in dieser Arbeit gesehen haben, verändern sich die Approximationseigenschaften der Näherungslösungen uh 2 V 0 h ( ), die man mit der Methode der finiten Elemente erhält, erheblich, wenn man vom Poisson- zum Hindernisproblem übergeht. Zwar erreicht man in beiden Fällen die H1-Ordnung O(h) (siehe Satz 3.2.1 und Korollar 3.2.2), sobald eine der Lp-Normen als Fehlermaß verwendet wird, tritt aber deutlich zu Tage, dass die in den Problemen (P) und (Ph) vorkommenden Nebenbedingungen den Fehler zwischen der exakten Lösung u und den Näherungen uh negativ beeinflussen. Wie diese Verschlechterung des Konvergenzverhaltens zustande kommt, haben wir in Abschnitt 6.1 beobachten können: Das grundlegende Problem ist einfach, dass sich lokal auftretende Effekte im Falle eines kontinuierlichen oder diskreten Hindernisproblems global auswirken können, wenn die Lösungen u und uh passend mit den Hindernissen und interagieren. Dies verhindert, dass der L2-Fehler analog zum Poisson-Problem mit der Ordnung O(h2) gegen Null geht, und führt dazu, dass man mit einer a priori Fehlerabschätzung der Form ku − uhkLq Ch im Allgemeinen nicht über die Ordnung O(h2−d/p) des L1-Fehlers aus dem Approximationssatz 2.1.5 hinauskommen kann. Dass die Gegenbeispiele, die wir in Abschnitt 6.1 betrachtet haben, dem Worst-Case entsprechen, haben wir in Kapitel 6 gesehen. Dort war es uns mit Hilfe des Konzeptes der diskreten Superlösung und unter Benutzung unserer Resultate zur einseitigen Finite-Elemente-Approximation möglich, zu zeigen, dass die Ordnung O(h2−d/p) in der L1-Norm – zumindest bis auf einen logarithmischen Faktor – immer erreicht wird, wenn die Lösung u in W2,p( ) ist und die verwendeten Triangulierungen der Bedingung (6.14) genügen. Hier ist auch deutlich geworden, dass man eigentlich ein Stabilitätsproblem löst, wenn man sich mit a priori Fehlerabschätzungen für das Problem (P) beschäftigt. Alle Fragen, die sich im Kontext der Fehleranalyse für das Hindernisproblem ergeben, konnten wir in dieser Arbeit natürlich nicht beantworten. Offen sind zum Beispiel noch die folgenden Punkte: - Wie weit kann die Nicht-Positivitäts-Bedingung (6.14) abgeschwächt werden, ohne dass Satz 6.2.4 seine Gültigkeit verliert? Hier müsste man auch noch einige Beispiele konstruieren, aus denen hervorgeht, wie positive Nebendiagonalelemente in den Systemmatrizen die Stabilität der diskreten Hindernisprobleme (Ph) beeinflussen. - Ist es im Höherdimensionalen eventuell doch möglich, in einer der Lq-Normen eine bessere Fehlerordnung als 2−d/p zu erreichen, oder lassen sich auch im Fall d > 1 Gegenbeispiele konstruieren, in denen sich der L1-Fehler zwischen den Hindernissen und in den Lq-Fehler zwischen u und uh fortpflanzt. Dies ist ein sehr interessantes Thema, denn möchte man im Mehrdimensionalen genauso vorgehen, wie wir es in Abschnitt 6.1 getan haben, dann muss man sich zum Beispiel mit der Frage beschäftigen, welche Hausdorff-Dimension die Menge haben muss, auf der das Maximum des Hindernisses bei der… Advisors/Committee Members: Meyer, Christian (advisor).

Subjects/Keywords: 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Christof, C. (2015). A priori Fehlerabschätzungen für die FE-Diskretisierung klassischer Hindernisprobleme. (Masters Thesis). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-16454

Chicago Manual of Style (16^th Edition):

Christof, Constantin. “A priori Fehlerabschätzungen für die FE-Diskretisierung klassischer Hindernisprobleme.” 2015. Masters Thesis, Technische Universität Dortmund. Accessed April 17, 2021. http://dx.doi.org/10.17877/DE290R-16454.

MLA Handbook (7^th Edition):

Christof, Constantin. “A priori Fehlerabschätzungen für die FE-Diskretisierung klassischer Hindernisprobleme.” 2015. Web. 17 Apr 2021.

Vancouver:

Christof C. A priori Fehlerabschätzungen für die FE-Diskretisierung klassischer Hindernisprobleme. [Internet] [Masters thesis]. Technische Universität Dortmund; 2015. [cited 2021 Apr 17]. Available from: http://dx.doi.org/10.17877/DE290R-16454.

Council of Science Editors:

Christof C. A priori Fehlerabschätzungen für die FE-Diskretisierung klassischer Hindernisprobleme. [Masters Thesis]. Technische Universität Dortmund; 2015. Available from: http://dx.doi.org/10.17877/DE290R-16454

Heriot-Watt University

28. Greer, Neil. The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems.

Degree: PhD, 2017, Heriot-Watt University

URL: http://hdl.handle.net/10399/3266

► In modern science and engineering there exist many heterogeneous problems, in which the material under consideration has non-uniform properties. For example when considering seepage under… (more)

▼ In modern science and engineering there exist many heterogeneous problems, in which the material under consideration has non-uniform properties. For example when considering seepage under a dam, water will flow at vastly different rates through sand and stone. Mathematically this can be represented as an elliptic boundary value problem that has a large jump in coefficients between subdomains. The optimised Schwarz method and the related two-Lagrange multiplier method are non-overlapping domain decomposition methods that can be used to numerically solve such boundary value problems. These methods work by solving local Robin problems on each subdomain in parallel, which then piece together to give an approximate solution to the global boundary value problem. It is known that with a careful choice of Robin parameter the convergence of these methods can be sped up. In this thesis we first review the known results for the optimised Schwarz method, deriving optimised Robin parameters and studying the asymptotic performance of the method as the mesh parameter of the discretisation is refined and the jump in coefficients becomes large. Next we formulate the two-Lagrange multiplier method for a model two subdomain problem and show its equivalence to the optimised Schwarz method under suitable conditions. The two-Lagrange multiplier method results in a non-symmetric linear system which is usually solved with a Krylov subspace method such as GMRES. The convergence of the GMRES method can be estimated by constructing a conformal map from the exterior of the field of values of the system matrix to the interior of the unit disc. We approximate the field of values of the two-Lagrange multiplier system matrix by a rectangle and calculate optimised Robin parameters that ensure the rectangle is “well conditioned” in the sense that GMRES converges quickly. We derive convergence estimates for GMRES and consider the behaviour asymptotically as the mesh size is refined and the jump in coefficients becomes large. The final part of the thesis is concerned with the case of heterogeneous problems with many subdomains and cross points, where three or more subdomains coincide. We formulate the two-Lagrange multiplier method for such problems and consider known preconditioners that are needed to improve convergence as the number of subdomains increases. Throughout the thesis numerical experiments are performed to verify the theoretical results.

Subjects/Keywords: 510

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APA (6^th Edition):

Greer, N. (2017). The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems. (Doctoral Dissertation). Heriot-Watt University. Retrieved from http://hdl.handle.net/10399/3266

Chicago Manual of Style (16^th Edition):

Greer, Neil. “The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems.” 2017. Doctoral Dissertation, Heriot-Watt University. Accessed April 17, 2021. http://hdl.handle.net/10399/3266.

MLA Handbook (7^th Edition):

Greer, Neil. “The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems.” 2017. Web. 17 Apr 2021.

Vancouver:

Greer N. The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems. [Internet] [Doctoral dissertation]. Heriot-Watt University; 2017. [cited 2021 Apr 17]. Available from: http://hdl.handle.net/10399/3266.

Council of Science Editors:

Greer N. The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems. [Doctoral Dissertation]. Heriot-Watt University; 2017. Available from: http://hdl.handle.net/10399/3266

University of Leeds

29. Almazaydeh, Asma Ibrahim A. Infinite Jordan permutation groups.

Degree: PhD, 2019, University of Leeds

URL: http://etheses.whiterose.ac.uk/24248/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.778708

► If G is a transitive permutation group on a set X, then G is a Jordan group if there is a partition of X into… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Almazaydeh, A. I. A. (2019). Infinite Jordan permutation groups. (Doctoral Dissertation). University of Leeds. Retrieved from http://etheses.whiterose.ac.uk/24248/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.778708

Chicago Manual of Style (16^th Edition):

Almazaydeh, Asma Ibrahim A. “Infinite Jordan permutation groups.” 2019. Doctoral Dissertation, University of Leeds. Accessed April 17, 2021. http://etheses.whiterose.ac.uk/24248/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.778708.

MLA Handbook (7^th Edition):

Almazaydeh, Asma Ibrahim A. “Infinite Jordan permutation groups.” 2019. Web. 17 Apr 2021.

Vancouver:

Almazaydeh AIA. Infinite Jordan permutation groups. [Internet] [Doctoral dissertation]. University of Leeds; 2019. [cited 2021 Apr 17]. Available from: http://etheses.whiterose.ac.uk/24248/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.778708.

Council of Science Editors:

Almazaydeh AIA. Infinite Jordan permutation groups. [Doctoral Dissertation]. University of Leeds; 2019. Available from: http://etheses.whiterose.ac.uk/24248/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.778708

University of Sheffield

30. Lu, Tao. Universal enveloping algebras of semi-direct products of Lie algebras and their quantum analogues.

Degree: PhD, 2016, University of Sheffield

URL: http://etheses.whiterose.ac.uk/13414/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689316

► The thesis consists of two parts. In the first part (Chapters 3 and 4), we study the universal enveloping algebra U(sl2 n V2) of the… (more)

Subjects/Keywords: 510

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APA (6^th Edition):

Lu, T. (2016). Universal enveloping algebras of semi-direct products of Lie algebras and their quantum analogues. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/13414/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689316

Chicago Manual of Style (16^th Edition):

Lu, Tao. “Universal enveloping algebras of semi-direct products of Lie algebras and their quantum analogues.” 2016. Doctoral Dissertation, University of Sheffield. Accessed April 17, 2021. http://etheses.whiterose.ac.uk/13414/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689316.

MLA Handbook (7^th Edition):

Lu, Tao. “Universal enveloping algebras of semi-direct products of Lie algebras and their quantum analogues.” 2016. Web. 17 Apr 2021.

Vancouver:

Lu T. Universal enveloping algebras of semi-direct products of Lie algebras and their quantum analogues. [Internet] [Doctoral dissertation]. University of Sheffield; 2016. [cited 2021 Apr 17]. Available from: http://etheses.whiterose.ac.uk/13414/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689316.

Council of Science Editors:

Lu T. Universal enveloping algebras of semi-direct products of Lie algebras and their quantum analogues. [Doctoral Dissertation]. University of Sheffield; 2016. Available from: http://etheses.whiterose.ac.uk/13414/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.689316

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