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1.
Zhang, Ran.
Fundamental solutions of a class of pseudo-differential operators with time-dependent negative definite symbols.
Degree: PhD, 2011, Swansea University
URL: https://cronfa.swan.ac.uk/Record/cronfa42643 
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752260
► In this thesis, we construct the fundamental solutions of pseudo-differential operators q(x,t,D) with time-dependent negative definite symbols q(x,t,xi) which are discussed as generators of Feller-…
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▼ In this thesis, we construct the fundamental solutions of pseudo-differential operators q(x,t,D) with time-dependent negative definite symbols q(x,t,xi) which are discussed as generators of Feller- and L2-sub-Markovian semigroups . The results are based on the Hille-Yosida theorem, the standard results of analytic semigroups of operators and the fundamental solutions of time-dependent parabolic equations.
Subjects/Keywords: 515
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APA (6th Edition):
Zhang, R. (2011). Fundamental solutions of a class of pseudo-differential operators with time-dependent negative definite symbols. (Doctoral Dissertation). Swansea University. Retrieved from https://cronfa.swan.ac.uk/Record/cronfa42643 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752260
Chicago Manual of Style (16th Edition):
Zhang, Ran. “Fundamental solutions of a class of pseudo-differential operators with time-dependent negative definite symbols.” 2011. Doctoral Dissertation, Swansea University. Accessed March 01, 2021.
https://cronfa.swan.ac.uk/Record/cronfa42643 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752260.
MLA Handbook (7th Edition):
Zhang, Ran. “Fundamental solutions of a class of pseudo-differential operators with time-dependent negative definite symbols.” 2011. Web. 01 Mar 2021.
Vancouver:
Zhang R. Fundamental solutions of a class of pseudo-differential operators with time-dependent negative definite symbols. [Internet] [Doctoral dissertation]. Swansea University; 2011. [cited 2021 Mar 01].
Available from: https://cronfa.swan.ac.uk/Record/cronfa42643 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752260.
Council of Science Editors:
Zhang R. Fundamental solutions of a class of pseudo-differential operators with time-dependent negative definite symbols. [Doctoral Dissertation]. Swansea University; 2011. Available from: https://cronfa.swan.ac.uk/Record/cronfa42643 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752260
Heriot-Watt University
2.
Christou, Chariton.
Investigation of volume diffusion hydrodynamics : application to tight porous media.
Degree: PhD, 2017, Heriot-Watt University
URL: http://hdl.handle.net/10399/3257
► Various engineering problems imply rarefied gas flows that rely in the transition and free molecular regimes, e.g., micro and nano devices. The recent expansion of…
(more)
▼ Various engineering problems imply rarefied gas flows that rely in the transition and free molecular regimes, e.g., micro and nano devices. The recent expansion of shale gas production where rarefied conditions are found in reservoirs exposed another area of application with a major importance. Continuum based methods like standard Navier- Stokes equations break down in the transition regime and free molecular regime. In order to model such flows discrete methods are usually adopted. Boltzmann equation can theoretically be used to simulate rarefied gas flows. However, complexity of its collision integral limits its applications mostly to simple cases (i.e., one dimension problems). The direct simulation Monte Carlo method which mimics the Boltzmann equation is the dominant method for simulating rarefied gas flows. It has been tested in several engineering problems, ranging from nano scale flow to re-entry vehicles with very consistent results in comparison with experimental data and analytical solutions. Its computational cost is, however, enormous for complex cases. Observations from Crookes radiometer inspired extending the continuum methods so that they could capture non-equilibrium phenomena in small scales. In the present thesis two different hydrodynamic model are presented. The first one is based on the Korteweg expression and the second one is called “Bi-velocity”. Firstly, the two models are presented in their mathematical forms. The proposed models are then developed in open-source computational fluid dynamics solvers. The models are tested and benchmarked in different rarefied gas flows problems in the whole range of Knudsen number. We used problems that are found in micro and nano systems and tight porous media. Results from the hydrodynamic models are compared against experimental data where available and the direct simulation Monte Carlo method. The two extended hydrodynamic models show improved results in comparison with standard Navier-Stokes.
Subjects/Keywords: 515
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APA (6th Edition):
Christou, C. (2017). Investigation of volume diffusion hydrodynamics : application to tight porous media. (Doctoral Dissertation). Heriot-Watt University. Retrieved from http://hdl.handle.net/10399/3257
Chicago Manual of Style (16th Edition):
Christou, Chariton. “Investigation of volume diffusion hydrodynamics : application to tight porous media.” 2017. Doctoral Dissertation, Heriot-Watt University. Accessed March 01, 2021.
http://hdl.handle.net/10399/3257.
MLA Handbook (7th Edition):
Christou, Chariton. “Investigation of volume diffusion hydrodynamics : application to tight porous media.” 2017. Web. 01 Mar 2021.
Vancouver:
Christou C. Investigation of volume diffusion hydrodynamics : application to tight porous media. [Internet] [Doctoral dissertation]. Heriot-Watt University; 2017. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10399/3257.
Council of Science Editors:
Christou C. Investigation of volume diffusion hydrodynamics : application to tight porous media. [Doctoral Dissertation]. Heriot-Watt University; 2017. Available from: http://hdl.handle.net/10399/3257
Heriot-Watt University
3.
Lijoka, Oluwaseun Francis.
Enriched discrete spaces for time domain wave equations.
Degree: PhD, 2017, Heriot-Watt University
URL: http://hdl.handle.net/10399/3264
► The second order linear wave equation is simple in representation but its numerical approximation is challenging, especially when the system contains waves of high frequencies.…
(more)
▼ The second order linear wave equation is simple in representation but its numerical approximation is challenging, especially when the system contains waves of high frequencies. While 10 grid points per wavelength is regarded as the rule of thumb to achieve tolerable approximation with the standard numerical approach, high resolution or high grid density is often required at high frequency which is often computationally demanding. As a contribution to tackling this problem, we consider in this thesis the discretization of the problem in the framework of the space-time discontinuous Galerkin (DG) method while investigating the solution in a finite dimensional space whose building blocks are waves themselves. The motivation for this approach is to reduce the number of degrees of freedom per wavelength as well as to introduce some analytical features of the problem into its numerical approximation. The developed space-time DG method is able to accommodate any polynomial bases. However, the Trefftz based space-time method proves to be efficient even for a system operating at high frequency. Comparison with polynomial spaces of total degree shows that equivalent orders of convergence are obtainable with fewer degrees of freedom. Moreover, the implementation of the Trefftz based method is cheaper as integration is restricted to the space-time mesh skeleton. We also extend our technique to a more complicated wave problem called the telegraph equation or the damped wave equation. The construction of the Trefftz space for this problem is not trivial. However, the exibility of the DG method enables us to use a special technique of propagating polynomial initial data using a wave-like solution (analytical) formula which gives us the required wave-like local solutions for the construction of the space. This thesis contains important a priori analysis as well as the convergence analysis for the developed space-time method, and extensive numerical experiments.
Subjects/Keywords: 515
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APA (6th Edition):
Lijoka, O. F. (2017). Enriched discrete spaces for time domain wave equations. (Doctoral Dissertation). Heriot-Watt University. Retrieved from http://hdl.handle.net/10399/3264
Chicago Manual of Style (16th Edition):
Lijoka, Oluwaseun Francis. “Enriched discrete spaces for time domain wave equations.” 2017. Doctoral Dissertation, Heriot-Watt University. Accessed March 01, 2021.
http://hdl.handle.net/10399/3264.
MLA Handbook (7th Edition):
Lijoka, Oluwaseun Francis. “Enriched discrete spaces for time domain wave equations.” 2017. Web. 01 Mar 2021.
Vancouver:
Lijoka OF. Enriched discrete spaces for time domain wave equations. [Internet] [Doctoral dissertation]. Heriot-Watt University; 2017. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10399/3264.
Council of Science Editors:
Lijoka OF. Enriched discrete spaces for time domain wave equations. [Doctoral Dissertation]. Heriot-Watt University; 2017. Available from: http://hdl.handle.net/10399/3264
4.
Towler, Kim.
Non-standard discretizations of differential equations.
Degree: PhD, 2015, University of Kent
URL: https://kar.kent.ac.uk/66665/
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739455
► This thesis explores non-standard numerical integration methods for a range of non-linear systems of differential equations with a particular interest in looking for the preservation…
(more)
▼ This thesis explores non-standard numerical integration methods for a range of non-linear systems of differential equations with a particular interest in looking for the preservation of various features when moving from the continuous system to a discrete setting. Firstly the exsiting non-standard schemes such as one discovered by Hirota and Kimura (and also Kahan) [21, 32] will be presented along with general rules for creating an effective numerical integration scheme devised by Mickens [40]. We then move on to the specific example of the Lotka-Volterra system and present a method for finding the most general forms of a non-standard scheme that is both symplectic and birational. The resulting three schemes found through this method have also been discovered through an alternative method by Roeger in [52]. Next we look at discretizing examples of 3-dimensional bi-Hamiltonian systems from a list given by G¨umral and Nutku [18] using the Hirota-Kimura/Kahan method followed by the same method applied to the H´enon-Heiles case (ii) system. The B¨acklund transformation for the H´enon-Heiles is also considered. Finally chapter 6 looks at systems with cubic vector fields and limit cycles with an aim to find the most general form of a non-standard scheme for two examples. First we look at a trimolecular system and then a Hamiltonian system that has a quartic potential.
Subjects/Keywords: 515
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APA (6th Edition):
Towler, K. (2015). Non-standard discretizations of differential equations. (Doctoral Dissertation). University of Kent. Retrieved from https://kar.kent.ac.uk/66665/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739455
Chicago Manual of Style (16th Edition):
Towler, Kim. “Non-standard discretizations of differential equations.” 2015. Doctoral Dissertation, University of Kent. Accessed March 01, 2021.
https://kar.kent.ac.uk/66665/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739455.
MLA Handbook (7th Edition):
Towler, Kim. “Non-standard discretizations of differential equations.” 2015. Web. 01 Mar 2021.
Vancouver:
Towler K. Non-standard discretizations of differential equations. [Internet] [Doctoral dissertation]. University of Kent; 2015. [cited 2021 Mar 01].
Available from: https://kar.kent.ac.uk/66665/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739455.
Council of Science Editors:
Towler K. Non-standard discretizations of differential equations. [Doctoral Dissertation]. University of Kent; 2015. Available from: https://kar.kent.ac.uk/66665/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739455
5.
Dowie, Ellen.
Rational solutions of nonlinear partial differential equations.
Degree: PhD, 2018, University of Kent
URL: https://kar.kent.ac.uk/66565/
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739518
► The work in this thesis considers rational solutions of nonlinear partial differential equations formed from polynomials. The main work will be on the Boussinesq equation…
(more)
▼ The work in this thesis considers rational solutions of nonlinear partial differential equations formed from polynomials. The main work will be on the Boussinesq equation and the Kadomtsev-Petviashvili-I (KP-I) equation, the nonlinear Schroedinger equation will also be included for completeness. Rational solutions of the Boussinesq equation model rogue wave behaviour. These solutions are shown to be highly structured which, it is hypothesised, is due to the inherent structure and form of integrable differential equations. Rogue wave solutions have been observed in equations such as the nonlinear Schrödinger equation, KP equation and the Boussinesq equation, to name but a few. By examining the form of these solutions and considering the behaviour of the roots, the aim is to establish the behaviour of this family of solutions. All solutions are bounded and real. Additionally, since a generating function for the KP equation solutions already exists, a characterisation of the solutions will be made along with an attempt at understanding the current generating function in order to improve its adaptability. Links between solutions of the three equations will be shown as well as a function that can solve all three equations subject to certain criteria on the parameters.
Subjects/Keywords: 515
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APA (6th Edition):
Dowie, E. (2018). Rational solutions of nonlinear partial differential equations. (Doctoral Dissertation). University of Kent. Retrieved from https://kar.kent.ac.uk/66565/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739518
Chicago Manual of Style (16th Edition):
Dowie, Ellen. “Rational solutions of nonlinear partial differential equations.” 2018. Doctoral Dissertation, University of Kent. Accessed March 01, 2021.
https://kar.kent.ac.uk/66565/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739518.
MLA Handbook (7th Edition):
Dowie, Ellen. “Rational solutions of nonlinear partial differential equations.” 2018. Web. 01 Mar 2021.
Vancouver:
Dowie E. Rational solutions of nonlinear partial differential equations. [Internet] [Doctoral dissertation]. University of Kent; 2018. [cited 2021 Mar 01].
Available from: https://kar.kent.ac.uk/66565/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739518.
Council of Science Editors:
Dowie E. Rational solutions of nonlinear partial differential equations. [Doctoral Dissertation]. University of Kent; 2018. Available from: https://kar.kent.ac.uk/66565/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739518
6.
Strathmann, Heiko.
Kernel methods for Monte Carlo.
Degree: PhD, 2018, University College London (University of London)
URL: https://discovery.ucl.ac.uk/id/eprint/10040707/
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747199
► This thesis investigates the use of reproducing kernel Hilbert spaces (RKHS) in the context of Monte Carlo algorithms. The work proceeds in three main themes.…
(more)
▼ This thesis investigates the use of reproducing kernel Hilbert spaces (RKHS) in the context of Monte Carlo algorithms. The work proceeds in three main themes. Adaptive Monte Carlo proposals: We introduce and study two adaptive Markov chain Monte Carlo (MCMC) algorithms to sample from target distributions with non-linear support and intractable gradients. Our algorithms, generalisations of random walk Metropolis and Hamiltonian Monte Carlo, adaptively learn local covariance and gradient structure respectively, by modelling past samples in an RKHS. We further show how to embed these methods into the sequential Monte Carlo framework. Efficient and principled score estimation: We propose methods for fitting an RKHS exponential family model that work by fitting the gradient of the log density, the score, thus avoiding the need to compute a normalization constant. While the problem is of general interest, here we focus on its embedding into the adaptive MCMC context from above. We improve the computational efficiency of an earlier solution with two novel fast approximation schemes without guarantees, and a low-rank, Nyström-like solution. The latter retains the consistency and convergence rates of the exact solution, at lower computational cost. Goodness-of-fit testing: We propose a non-parametric statistical test for goodness-of-fit. The measure is a divergence constructed via Stein's method using functions from an RKHS. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, and apply the test to quantifying convergence of approximate MCMC methods, statistical model criticism, and evaluating accuracy in non-parametric score estimation.
Subjects/Keywords: 515
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APA ·
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APA (6th Edition):
Strathmann, H. (2018). Kernel methods for Monte Carlo. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/10040707/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747199
Chicago Manual of Style (16th Edition):
Strathmann, Heiko. “Kernel methods for Monte Carlo.” 2018. Doctoral Dissertation, University College London (University of London). Accessed March 01, 2021.
https://discovery.ucl.ac.uk/id/eprint/10040707/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747199.
MLA Handbook (7th Edition):
Strathmann, Heiko. “Kernel methods for Monte Carlo.” 2018. Web. 01 Mar 2021.
Vancouver:
Strathmann H. Kernel methods for Monte Carlo. [Internet] [Doctoral dissertation]. University College London (University of London); 2018. [cited 2021 Mar 01].
Available from: https://discovery.ucl.ac.uk/id/eprint/10040707/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747199.
Council of Science Editors:
Strathmann H. Kernel methods for Monte Carlo. [Doctoral Dissertation]. University College London (University of London); 2018. Available from: https://discovery.ucl.ac.uk/id/eprint/10040707/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747199
University of Oxford
7.
Baird, Graham.
Mixed discrete-continuous fragmentation equations.
Degree: PhD, 2017, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740847
► The work contained in this thesis concerns the development, and the mathematical and numerical analysis, of a new class of hybrid discrete-continuous fragmentation model. The…
(more)
▼ The work contained in this thesis concerns the development, and the mathematical and numerical analysis, of a new class of hybrid discrete-continuous fragmentation model. The framework is introduced as a potential answer to the occurrence of 'shattering' mass loss, commonly observed in purely continuous fragmentation models. Initially, the study begins by introducing the model, which takes the form of an integro-differential equation, coupled with a system of ordinary differential equations. Once the model has been established, it is subjected to a rigorous mathematical analysis, using the theory and methods of operator semigroups and their generators. Most notably, by applying the theory relating to the Kato-Voigt perturbation theorem, honest substochastic semigroups and operator matrices, the existence of a unique, differentiable solution to the model is established. This solution is also shown to preserve non-negativity and conserve mass. Having determined the existence of a solution, the work continues with the development of a numerical scheme for the approximate solution of the modelling equations. Considering a truncated version of the equations, rewritten in an alternative conservative form, the scheme is built around a finite volume discretisation. Using a standard weak compactness argument, the approximations generated by the numerical scheme are shown to converge (weakly) to a weak solution of the truncated equations. By relating this weak solution to the strong solutions provided by the earlier semigroup analysis, the weak solution is found to be unique and as a consequence, differentiable, non-negative and mass-conserving. The theoretical study is completed with an examination of the effect of varying the truncation point. In particular, establishing that as the length of the truncated interval is increased, in the limit, the original solution to the full model is obtained. Finally, the thesis is completed with a numerical investigation, seeking to experimentally confirm the assertions of the earlier theoretical work and assess the performance of the numerical scheme for a suite of test models.
Subjects/Keywords: 515
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APA (6th Edition):
Baird, G. (2017). Mixed discrete-continuous fragmentation equations. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740847
Chicago Manual of Style (16th Edition):
Baird, Graham. “Mixed discrete-continuous fragmentation equations.” 2017. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740847.
MLA Handbook (7th Edition):
Baird, Graham. “Mixed discrete-continuous fragmentation equations.” 2017. Web. 01 Mar 2021.
Vancouver:
Baird G. Mixed discrete-continuous fragmentation equations. [Internet] [Doctoral dissertation]. University of Oxford; 2017. [cited 2021 Mar 01].
Available from: https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740847.
Council of Science Editors:
Baird G. Mixed discrete-continuous fragmentation equations. [Doctoral Dissertation]. University of Oxford; 2017. Available from: https://ora.ox.ac.uk/objects/uuid:311da0da-6801-4120-9129-d95786a153b6 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740847
University of Cambridge
8.
Low, Zhen Lin.
Categories of spaces built from local models.
Degree: PhD, 2016, University of Cambridge
URL: https://doi.org/10.17863/CAM.384
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690886
► Many of the classes of objects studied in geometry are defined by first choosing a class of nice spaces and then allowing oneself to glue…
(more)
▼ Many of the classes of objects studied in geometry are defined by first choosing a class of nice spaces and then allowing oneself to glue these local models together to construct more general spaces. The most well-known examples are manifolds and schemes. The main purpose of this thesis is to give a unified account of this procedure of constructing a category of spaces built from local models and to study the general properties of such categories of spaces. The theory developed here will be illustrated with reference to examples, including the aforementioned manifolds and schemes. For concreteness, consider the passage from commutative rings to schemes. There are three main steps: first, one identifies a distinguished class of ring homomorphisms corresponding to open immersions of schemes; second, one defines the notion of an open covering in terms of these distinguished homomorphisms; and finally, one embeds the opposite of the category of commutative rings in an ambient category in which one can glue (the formal duals of) commutative rings along (the formal duals of) distinguished homomorphisms. Traditionally, the ambient category is taken to be the category of locally ringed spaces, but following Grothendieck, one could equally well work in the category of sheaves for the large Zariski site—this is the so-called ‘functor of points approach’. A third option, related to the exact completion of a category, is described in this thesis. The main result can be summarised thus: categories of spaces built from local models are extensive categories with a class of distinguished morphisms, subject to various stability axioms, such that certain equivalence relations (defined relative to the class of distinguished morphisms) have pullback-stable quotients; moreover, this construction is functorial and has a universal property.
Subjects/Keywords: 515
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APA (6th Edition):
Low, Z. L. (2016). Categories of spaces built from local models. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.384 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690886
Chicago Manual of Style (16th Edition):
Low, Zhen Lin. “Categories of spaces built from local models.” 2016. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.384 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690886.
MLA Handbook (7th Edition):
Low, Zhen Lin. “Categories of spaces built from local models.” 2016. Web. 01 Mar 2021.
Vancouver:
Low ZL. Categories of spaces built from local models. [Internet] [Doctoral dissertation]. University of Cambridge; 2016. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.384 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690886.
Council of Science Editors:
Low ZL. Categories of spaces built from local models. [Doctoral Dissertation]. University of Cambridge; 2016. Available from: https://doi.org/10.17863/CAM.384 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690886
9.
Dietert, Helge.
Contributions to mixing and hypocoercivity in kinetic models.
Degree: PhD, 2017, University of Cambridge
URL: https://doi.org/10.17863/CAM.7765
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707790
► The main results of my work contribute to the mathematical study of a stability mechanism common to both the Vlasov–Poisson equation and the Kuramoto equation.…
(more)
▼ The main results of my work contribute to the mathematical study of a stability mechanism common to both the Vlasov–Poisson equation and the Kuramoto equation. These kinetic models come from very different areas of physics: the Vlasov–Poisson equation models plasmas and the Kuramoto equation models synchronisation behaviour. The stability was first described by Landau in 1946 and is a subtle behaviour, because the damping only happens in a suitably weak sense. In fact, the models are not dissipative and cannot be stable in a strong topology. Instead, the so-called Landau damping happens through phase mixing. My contributions include a simplified linear analysis for the Vlasov–Poisson equation around the spatially homogeneous state. For the Kuramoto equation, I cover the linear analysis around general stationary states and show nonlinear stability results with algebraic and exponential decay. Moreover, I show how the mean-field estimate by Dobrushin can be improved around the incoherent state. In addition, I study how a kinetic system can reach a thermal equilibrium. This is modelled by adding a dissipative term, which by itself drives the system to a local equilibrium. In hypocoercivity theory, the complementary effect of the transport operator is used to show exponential decay to a global equilibrium. In particular, I show how a probabilistic treatment can complement the standard hypocoercivity theory, which constructs equivalent norms, and I discuss the necessity of the geometric control condition for the spatially degenerate kinetic Fokker–Planck equation. Finally, I study the possible discretisation of the velocity variable for kinetic equations. For the numerical stability, Hermite functions are a suitable choice, because their differentiation matrix is skew-symmetric. However, so far a fast expansion algorithm has been lacking and this is addressed in this work.
Subjects/Keywords: 515
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APA ·
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Manager
APA (6th Edition):
Dietert, H. (2017). Contributions to mixing and hypocoercivity in kinetic models. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.7765 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707790
Chicago Manual of Style (16th Edition):
Dietert, Helge. “Contributions to mixing and hypocoercivity in kinetic models.” 2017. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.7765 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707790.
MLA Handbook (7th Edition):
Dietert, Helge. “Contributions to mixing and hypocoercivity in kinetic models.” 2017. Web. 01 Mar 2021.
Vancouver:
Dietert H. Contributions to mixing and hypocoercivity in kinetic models. [Internet] [Doctoral dissertation]. University of Cambridge; 2017. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.7765 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707790.
Council of Science Editors:
Dietert H. Contributions to mixing and hypocoercivity in kinetic models. [Doctoral Dissertation]. University of Cambridge; 2017. Available from: https://doi.org/10.17863/CAM.7765 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707790
University of Cambridge
10.
Mathews, James Richard.
Mathematical modelling of noise generation in turbofan aeroengines using Green's functions.
Degree: PhD, 2016, University of Cambridge
URL: https://doi.org/10.17863/CAM.8962
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715942
► With demand for aircraft travel set to double in the next twenty years, targets are in place to reduce noise levels and emissions. For example,…
(more)
▼ With demand for aircraft travel set to double in the next twenty years, targets are in place to reduce noise levels and emissions. For example, one target is that the effective perceived noise from aircraft in 2020 should be half of the 2000 level. One of the key noise components is the aeroengine. Building and designing an aeroengine costs millions of pounds and furthermore, to prove the aeroengine is safe, it has to be tested to destruction. Engineers and mathematicians are employed to design aeroengines that will not only be quieter but more fuel efficient and produce fewer harmful emissions while maintaining or improving performance. The main topic of this thesis is investigating rotor-stator interaction which occurs when the turbulent, swirling air produced by the rotor hits the stator and generates noise. We do this in two distinct ways, firstly we calculate the Green’s function for pressure in a turbofan duct with swirling mean flow and secondly we investigate the effect of turbulence hitting an isolated aerofoil. The Green’s function allows engineers to calculate the noise from rotor-stator interaction in simple cases and can be used in beamforming to analyse noise sources in the aeroengine. We consider an infinite duct, and use the Euler equations to derive a sixth order partial differential equation for pressure in the duct. We then find a Green’s function of this equation, which can be done numerically or analytically using high-frequency asymptotics. Our main interest is the analytic Green’s function, which we compare to numerical results. We begin by assuming the base flow has shear and swirling components in a constantly lined duct, and our analytic Green’s function is a new result. We then calculate the Green’s function for a base flow with variable entropy and a lining that varies with circumferential position. To consider flow-blade interaction we simulate the turbulent wake of the rotor hitting a single stator blade. Tests in wind tunnels have shown that, depending on the parameters, introducing a serration on the leading edge of the aerofoil can reduce the noise significantly. We build an analytical model to investigate the effect of the serrated edge, which again involves solving a differential equation by using a Green’s function. It also requires modelling the turbulence, which we do by using either deterministic eddies or stochastic eddies. We show it is possible to reduce the noise by using a serrated leading edge, but it is hard to predict the correct choice of serration to minimise the noise.
Subjects/Keywords: 515
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APA (6th Edition):
Mathews, J. R. (2016). Mathematical modelling of noise generation in turbofan aeroengines using Green's functions. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.8962 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715942
Chicago Manual of Style (16th Edition):
Mathews, James Richard. “Mathematical modelling of noise generation in turbofan aeroengines using Green's functions.” 2016. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.8962 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715942.
MLA Handbook (7th Edition):
Mathews, James Richard. “Mathematical modelling of noise generation in turbofan aeroengines using Green's functions.” 2016. Web. 01 Mar 2021.
Vancouver:
Mathews JR. Mathematical modelling of noise generation in turbofan aeroengines using Green's functions. [Internet] [Doctoral dissertation]. University of Cambridge; 2016. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.8962 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715942.
Council of Science Editors:
Mathews JR. Mathematical modelling of noise generation in turbofan aeroengines using Green's functions. [Doctoral Dissertation]. University of Cambridge; 2016. Available from: https://doi.org/10.17863/CAM.8962 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715942
11.
Tanzi, Matteo.
Heterogeneously coupled maps : from high to low dimensional systems through ergodic theory.
Degree: PhD, 2017, Imperial College London
URL: https://doi.org/10.25560/50709
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724197
► In this thesis we study ergodic theoretical properties of high-dimensional systems coupled on graphs. The local dynamics at each node is hyperbolic and coupled with…
(more)
▼ In this thesis we study ergodic theoretical properties of high-dimensional systems coupled on graphs. The local dynamics at each node is hyperbolic and coupled with other nodes according to the edges of the graph. We focus our attention on the case of graphs with heterogeneous degrees meaning that most of the nodes make a small number of interactions, while a few hub nodes have very high degree. For such high-dimensional systems there is a regime of the interaction strength for which the coupling is small for poorly connected systems, and large for the hub nodes. In particular, global hyperbolicity might be lost. We show that, under certain hypotheses, the dynamics of hub nodes can be very well approximated by a low-dimensional system for exponentially long time in the size of the network and that the system exhibit hyperbolic behaviour in this time window. Even if this describes only a long transient, we argue that this is the behaviour that one expects to observe in experiments. Such a description allows us to establish the emergence of macroscopic behaviour such as coherence of dynamics among hubs of the same connectivity layer (i.e. with the same number of connections). The HCM we study provide a new paradigm to explain why and how the dynamics of a network dynamical system can change across layers.
Subjects/Keywords: 515
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APA (6th Edition):
Tanzi, M. (2017). Heterogeneously coupled maps : from high to low dimensional systems through ergodic theory. (Doctoral Dissertation). Imperial College London. Retrieved from https://doi.org/10.25560/50709 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724197
Chicago Manual of Style (16th Edition):
Tanzi, Matteo. “Heterogeneously coupled maps : from high to low dimensional systems through ergodic theory.” 2017. Doctoral Dissertation, Imperial College London. Accessed March 01, 2021.
https://doi.org/10.25560/50709 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724197.
MLA Handbook (7th Edition):
Tanzi, Matteo. “Heterogeneously coupled maps : from high to low dimensional systems through ergodic theory.” 2017. Web. 01 Mar 2021.
Vancouver:
Tanzi M. Heterogeneously coupled maps : from high to low dimensional systems through ergodic theory. [Internet] [Doctoral dissertation]. Imperial College London; 2017. [cited 2021 Mar 01].
Available from: https://doi.org/10.25560/50709 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724197.
Council of Science Editors:
Tanzi M. Heterogeneously coupled maps : from high to low dimensional systems through ergodic theory. [Doctoral Dissertation]. Imperial College London; 2017. Available from: https://doi.org/10.25560/50709 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724197
University of Oxford
12.
Konieczny, Jakub.
On combinatorial properties of nil-Bohr sets of integers and related problems.
Degree: PhD, 2017, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:5afe1811-b37b-49a4-aecf-882f8ca0fb87
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729154
► This thesis deals with six problems in additive combinatorics and ergodic theory. A brief introduction to this general area and a summary of included results…
(more)
▼ This thesis deals with six problems in additive combinatorics and ergodic theory. A brief introduction to this general area and a summary of included results is given in Chapter I. In Chapter II, we consider sets of the form { n ϵ ℕ0 | |p(n) mod 1| ≤ ϵ (n) }, where p is a polynomial and ϵ(n) ≥ 0. We obtain various conditions under which any sufficiently large integer can be represented as a sum of 2 or 3 elements of a given set of this form. In Chapter III, we study the class of weakly mixing sets of integers, and prove that a certain class of polynomial equations can always be solved in such a set. In Chapter IV, we show that any nil – Bohr set contains a certain type of an additive pattern. Combined with earlier results of Host and Kra, his leads to a partial combinatorial characterisation of nil – Bohr sets. In Chapter V, we study the combinatorial properties of generalised polynomials (expressions built from polynomials and the floor function). In contrast with results of Bergelson and Leibman, we show that if the set of integers where a given generalised polynomial takes a non-zero value has asymptotic density 0, then it does not contain any IP set. This leads to a partial characterisation of automatic sequences which are given by generalised polynomial formulas. In Chapter V, we estimate the Gowers norms of the Thue-Morse sequence and the Rudin-Shapiro sequence. This gives some of the simplest deterministic examples of sequences with small Gowers norms of all orders.
Subjects/Keywords: 515
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APA (6th Edition):
Konieczny, J. (2017). On combinatorial properties of nil-Bohr sets of integers and related problems. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:5afe1811-b37b-49a4-aecf-882f8ca0fb87 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729154
Chicago Manual of Style (16th Edition):
Konieczny, Jakub. “On combinatorial properties of nil-Bohr sets of integers and related problems.” 2017. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
https://ora.ox.ac.uk/objects/uuid:5afe1811-b37b-49a4-aecf-882f8ca0fb87 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729154.
MLA Handbook (7th Edition):
Konieczny, Jakub. “On combinatorial properties of nil-Bohr sets of integers and related problems.” 2017. Web. 01 Mar 2021.
Vancouver:
Konieczny J. On combinatorial properties of nil-Bohr sets of integers and related problems. [Internet] [Doctoral dissertation]. University of Oxford; 2017. [cited 2021 Mar 01].
Available from: https://ora.ox.ac.uk/objects/uuid:5afe1811-b37b-49a4-aecf-882f8ca0fb87 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729154.
Council of Science Editors:
Konieczny J. On combinatorial properties of nil-Bohr sets of integers and related problems. [Doctoral Dissertation]. University of Oxford; 2017. Available from: https://ora.ox.ac.uk/objects/uuid:5afe1811-b37b-49a4-aecf-882f8ca0fb87 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729154
University of Oxford
13.
Gmeineder, Franz Xaver.
Regularity theory for variational problems on BD.
Degree: PhD, 2017, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:1f412087-de70-44a8-a045-8923f1e29611
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729064
► In this thesis we provide regularity results for convex and semiconvex variational problems which are of linear growth and depend on the symmetric rather than…
(more)
▼ In this thesis we provide regularity results for convex and semiconvex variational problems which are of linear growth and depend on the symmetric rather than the full gradient. By the non-availability of Korn's Inequality (known as Ornstein's Non-Inequality), usual approaches need to be modified in order to obtain higher regularity of generalised minima.
Subjects/Keywords: 515
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APA ·
Chicago ·
MLA ·
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CSE |
Export
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APA (6th Edition):
Gmeineder, F. X. (2017). Regularity theory for variational problems on BD. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:1f412087-de70-44a8-a045-8923f1e29611 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729064
Chicago Manual of Style (16th Edition):
Gmeineder, Franz Xaver. “Regularity theory for variational problems on BD.” 2017. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
https://ora.ox.ac.uk/objects/uuid:1f412087-de70-44a8-a045-8923f1e29611 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729064.
MLA Handbook (7th Edition):
Gmeineder, Franz Xaver. “Regularity theory for variational problems on BD.” 2017. Web. 01 Mar 2021.
Vancouver:
Gmeineder FX. Regularity theory for variational problems on BD. [Internet] [Doctoral dissertation]. University of Oxford; 2017. [cited 2021 Mar 01].
Available from: https://ora.ox.ac.uk/objects/uuid:1f412087-de70-44a8-a045-8923f1e29611 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729064.
Council of Science Editors:
Gmeineder FX. Regularity theory for variational problems on BD. [Doctoral Dissertation]. University of Oxford; 2017. Available from: https://ora.ox.ac.uk/objects/uuid:1f412087-de70-44a8-a045-8923f1e29611 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729064
University of Oxford
14.
Chonev, Ventsislav.
Reachability problems for linear dynamical systems.
Degree: PhD, 2015, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:e73d1a5b-edce-4e1d-a593-fd8df7e2a817
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730585
► The object of principal interest in this thesis is linear dynamical systems: deterministic systems which evolve under a linear operator. They are specified by an…
(more)
▼ The object of principal interest in this thesis is linear dynamical systems: deterministic systems which evolve under a linear operator. They are specified by an initial state set I, contained in ℝm, and a real m-by-m evolution matrix A. We distinguish two varieties of linear dynamical systems: discrete-time and continuous-time. In the discrete-time setting, the state x(n) of the system at time n for natural n is governed by the difference equation x(n)=Ax(n-1). Similarly, in the continuous case, the state x(t) at real, non-negative times t is determined by a system of first-order linear differential equations: x'(t) = Ax(t). In both cases, x(0) lies in I. Throughout this thesis, we will be interested in the Reachability Problem for linear dynamical systems, which may be formulated in a general way as follows: given a target set T contained in ℝm and a (discrete- or continuous-time) linear dynamical system specified by the evolution matrix <b>A</b> and the set of initial states I, determine whether for all x(0) in I, starting from x(0), the system will eventually be in a state which lies in T. In order to make the decision problem well-defined, one must first fix an admissible class of initial sets and, similarly, a class of target sets of interest. For the purposes of expressing the problem instance, it is also necessary to restrict the domain of the input data to a subset of the reals which may be represented effectively, such as the rational numbers or the algebraic numbers. As we vary the choice of domain, the types of initial and target sets under consideration and the discreteness of time, a rich landscape of decision problems emerges. The goal of the present thesis is to explore pointwise reachability problems, that is, reachability from a single initial state. Under the assumption that I consists of a single point in ℝm provided as part of the input data, we will study reachability to polyhedral targets, in the context of both discrete- and continuous-time linear dynamical systems. We prove both upper complexity bounds and hardness results, employing in the process a wide-ranging arsenal of techniques and mathematical tools. We rely on powerful number-theoretic results, such as Baker's Theorem on inhomogeneous linear forms of logarithms of algebraic numbers, Schanuel's Conjecture on the transcendence degree of certain field extensions of the rationals, and Kronecker's Theorem on simultaneous inhomogeneous Diophantine approximation. We draw interesting connections with the study of linear recurrence sequences and exponential polynomials, and relate pointwise reachability to open problems concerning the approximability by rationals of algebraic numbers and logarithms of algebraic numbers. Albeit a simple model, linear dynamical systems are of profound interest, both from a theoretical and a practical standpoint. Reachability problems for linear dynamical systems have recently elicited considerable attention, due to their frequent occurrence in practice and their…
Subjects/Keywords: 515
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APA ·
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Export
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Manager
APA (6th Edition):
Chonev, V. (2015). Reachability problems for linear dynamical systems. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:e73d1a5b-edce-4e1d-a593-fd8df7e2a817 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730585
Chicago Manual of Style (16th Edition):
Chonev, Ventsislav. “Reachability problems for linear dynamical systems.” 2015. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
https://ora.ox.ac.uk/objects/uuid:e73d1a5b-edce-4e1d-a593-fd8df7e2a817 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730585.
MLA Handbook (7th Edition):
Chonev, Ventsislav. “Reachability problems for linear dynamical systems.” 2015. Web. 01 Mar 2021.
Vancouver:
Chonev V. Reachability problems for linear dynamical systems. [Internet] [Doctoral dissertation]. University of Oxford; 2015. [cited 2021 Mar 01].
Available from: https://ora.ox.ac.uk/objects/uuid:e73d1a5b-edce-4e1d-a593-fd8df7e2a817 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730585.
Council of Science Editors:
Chonev V. Reachability problems for linear dynamical systems. [Doctoral Dissertation]. University of Oxford; 2015. Available from: https://ora.ox.ac.uk/objects/uuid:e73d1a5b-edce-4e1d-a593-fd8df7e2a817 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730585
University of Oxford
15.
Boutaib, Youness.
Lipschitz geometry and rough paths.
Degree: PhD, 2016, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:ebd0dfdb-fd8f-42fa-80f7-7707df695117
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728898
► Motivated by building a Lipschitz structure on the reachability set of a set of rough differential equations, we study first Lipschitz maps in full detail…
(more)
▼ Motivated by building a Lipschitz structure on the reachability set of a set of rough differential equations, we study first Lipschitz maps in full detail and in many aspects: we show embedding properties of Lipschitz spaces, study algebraic properties, local versus global behaviour of Lipschitz maps, give a version of the inverse function and the constant rank theorems and analyse flows of Lipschitz vector fields. Along the way, we give quantitative estimates, which is, after all, one of the main strengths of the Lipschitz geometry. Second, we combine our observations on the local properties of rough paths and Lipschitz maps to give a rather flexible structure on manifolds that allow the definition of rough paths on them and explain how the same process can be used to define a notion of coloured paths on manifolds, assuming that one can build a suitable functorial rule. Finally, we make use of those remarks to derive a quantitative condition that endow orbits of vector fields with the structure of a Lipschitz manifold and show, that under this condition, the space of solutions of rough differential equations driven by rough paths is the same as the one we obtain by driving the RDEs with smooth paths.
Subjects/Keywords: 515
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APA ·
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MLA ·
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Export
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APA (6th Edition):
Boutaib, Y. (2016). Lipschitz geometry and rough paths. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:ebd0dfdb-fd8f-42fa-80f7-7707df695117 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728898
Chicago Manual of Style (16th Edition):
Boutaib, Youness. “Lipschitz geometry and rough paths.” 2016. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
http://ora.ox.ac.uk/objects/uuid:ebd0dfdb-fd8f-42fa-80f7-7707df695117 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728898.
MLA Handbook (7th Edition):
Boutaib, Youness. “Lipschitz geometry and rough paths.” 2016. Web. 01 Mar 2021.
Vancouver:
Boutaib Y. Lipschitz geometry and rough paths. [Internet] [Doctoral dissertation]. University of Oxford; 2016. [cited 2021 Mar 01].
Available from: http://ora.ox.ac.uk/objects/uuid:ebd0dfdb-fd8f-42fa-80f7-7707df695117 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728898.
Council of Science Editors:
Boutaib Y. Lipschitz geometry and rough paths. [Doctoral Dissertation]. University of Oxford; 2016. Available from: http://ora.ox.ac.uk/objects/uuid:ebd0dfdb-fd8f-42fa-80f7-7707df695117 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728898
University of Oxford
16.
Rotaetxe, Julen.
Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations.
Degree: PhD, 2016, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:e0d3915d-0467-4a1b-9b3b-7d511df405f0
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730303
► We analyse two practical aspects that arise in the numerical solution of Hamilton-Jacobi-Bellman (HJB) equations by a particular class of monotone approximation schemes known as…
(more)
▼ We analyse two practical aspects that arise in the numerical solution of Hamilton-Jacobi-Bellman (HJB) equations by a particular class of monotone approximation schemes known as semi-Lagrangian schemes, namely boundary treatment and multigrid preconditioning. These schemes make use of a wide stencil to achieve convergence and result in discretization matrices that are less sparse and less local than those coming from standard finite difference schemes. This leads to computational difficulties not encountered there. We start by considering the overstepping of the domain boundary and analyse the accuracy and stability of stencil truncation. This truncation imposes a stricter CFL condition for explicit schemes in the vicinity of boundaries than in the interior, such that implicit schemes become attractive. Then, we show that for problems posed on a (semi) infinite domain whose boundary has no regular points we can avoid such truncation by means of a smooth transformation of the domain. Next, we consider the error analysis for semi-Lagrangian schemes with truncated stencils. The stencil truncation alters properties of the semi-Lagrangian scheme that were used for the derivation of error bounds. Hence, using an alternative approach, relying on a regularization procedure due to Krylov and a switching system approximation to the HJB equation, we derive error bounds for the truncated scheme. Finally, motivated by the stricter CFL condition of the scheme with truncated stencils, we consider implicit time stepping schemes. This involves solving non-linear systems of algebraic equations for semi-Lagrangian discretization matrices, hence, we study the use of geometric, algebraic and aggregation-based multigrid preconditioners to construct efficient solvers.
Subjects/Keywords: 515
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APA ·
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MLA ·
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Export
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APA (6th Edition):
Rotaetxe, J. (2016). Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:e0d3915d-0467-4a1b-9b3b-7d511df405f0 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730303
Chicago Manual of Style (16th Edition):
Rotaetxe, Julen. “Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations.” 2016. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
http://ora.ox.ac.uk/objects/uuid:e0d3915d-0467-4a1b-9b3b-7d511df405f0 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730303.
MLA Handbook (7th Edition):
Rotaetxe, Julen. “Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations.” 2016. Web. 01 Mar 2021.
Vancouver:
Rotaetxe J. Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations. [Internet] [Doctoral dissertation]. University of Oxford; 2016. [cited 2021 Mar 01].
Available from: http://ora.ox.ac.uk/objects/uuid:e0d3915d-0467-4a1b-9b3b-7d511df405f0 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730303.
Council of Science Editors:
Rotaetxe J. Boundary treatment and multigrid preconditioning for semi-Lagrangian schemes applied to Hamilton-Jacobi-Bellman equations. [Doctoral Dissertation]. University of Oxford; 2016. Available from: http://ora.ox.ac.uk/objects/uuid:e0d3915d-0467-4a1b-9b3b-7d511df405f0 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730303
University of Oxford
17.
Ahmadi, Mohamadreza.
Analysis of systems described by partial differential equations using convex optimization.
Degree: PhD, 2016, University of Oxford
URL: http://ora.ox.ac.uk/objects/uuid:ae952a10-7602-4f61-9b8f-60350c90d4dc
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728935
► In this dissertation, computational methods based on convex optimization, for the analysis of systems described by partial differential equations (PDEs), are proposed. Firstly, motivated by…
(more)
▼ In this dissertation, computational methods based on convex optimization, for the analysis of systems described by partial differential equations (PDEs), are proposed. Firstly, motivated by the integral inequalities encountered in the Lyapunov stability analysis of PDEs, a method based on sum-of-squares (SOS) programming is proposed to verify integral inequalities with polynomial integrands. This method parallels the schemes based on linear matrix inequalities (LMIs) for the analysis of linear systems and approaches based on SOS programming for the analysis of polynomial nonlinear systems. Secondly, dissipation inequalities for input-state/output analysis of PDE systems are formulated. Similar to the case of systems described by ordinary differential equations (ODEs), it is demonstrated that the dissipation inequalities can be used to check inputstate/ output properties, such as passivity, reachability, induced norms, and input-to-state stability (ISS). Furthermore, it is shown that the proposed input-state/output analysis method based on dissipation inequalities allows one to infer properties of interconnected PDE-PDE or PDE-ODE systems. In this regard, interconnections at the boundaries and interconnections over the domain are considered. It is also shown that an appropriate choice of the storage functional structure casts the dissipation inequalities into integral inequalities, which can be checked via convex optimization. Thirdly, a method is proposed for safety verification of PDE systems. That is, the problem of checking whether all the solutions of a PDE, starting from a given set of initial conditions, do not enter some undesired or unsafe set. The method hinges on an extension of barrier certificates to infinite-dimensional systems. To this end, a functional of the states of the PDE called the barrier functional is introduced. If this functional satisfies two inequalities along the solutions of the PDE, then the safety of the solutions is verified. If the barrier functional takes the form of an integral functional, the inequalities convert to integral inequalities that can be checked using convex optimization in the case of polynomial data. Furthermore, the proposed safety verification method is used for bounding output functionals of PDEs. Finally, the tools developed in this dissertation are applied to study the stability and input-output analysis problems of fluid flows. In particular, incompressible viscous flows with constant perturbations in one of the coordinates are studied. The stability and inputoutput analysis is based on Lyapunov and dissipativity theories, respectively, and subsumes exponential stability, energy amplification, worst case input amplification and ISS. To the author's knowledge, this is the first time that ISS of flow models is being studied. It is shown that an appropriate choice of the Lyapunov/storage functional leads to integral inequalities with quadratic integrands. For polynomial base flows and polynomial data on flow geometry, the integral inequalities can be solved using…
Subjects/Keywords: 515
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APA (6th Edition):
Ahmadi, M. (2016). Analysis of systems described by partial differential equations using convex optimization. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:ae952a10-7602-4f61-9b8f-60350c90d4dc ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728935
Chicago Manual of Style (16th Edition):
Ahmadi, Mohamadreza. “Analysis of systems described by partial differential equations using convex optimization.” 2016. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
http://ora.ox.ac.uk/objects/uuid:ae952a10-7602-4f61-9b8f-60350c90d4dc ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728935.
MLA Handbook (7th Edition):
Ahmadi, Mohamadreza. “Analysis of systems described by partial differential equations using convex optimization.” 2016. Web. 01 Mar 2021.
Vancouver:
Ahmadi M. Analysis of systems described by partial differential equations using convex optimization. [Internet] [Doctoral dissertation]. University of Oxford; 2016. [cited 2021 Mar 01].
Available from: http://ora.ox.ac.uk/objects/uuid:ae952a10-7602-4f61-9b8f-60350c90d4dc ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728935.
Council of Science Editors:
Ahmadi M. Analysis of systems described by partial differential equations using convex optimization. [Doctoral Dissertation]. University of Oxford; 2016. Available from: http://ora.ox.ac.uk/objects/uuid:ae952a10-7602-4f61-9b8f-60350c90d4dc ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728935
University of Oxford
18.
Geyer, Felix.
Improving properties of operators by extensions and reductions.
Degree: PhD, 2015, University of Oxford
URL: https://ora.ox.ac.uk/objects/uuid:f2978369-108e-4143-9000-50a11c973e83
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712095
► This thesis presents and develops two tools which can be used to work with lower bounds of operators. One tool in working with lower bounds…
(more)
▼ This thesis presents and develops two tools which can be used to work with lower bounds of operators. One tool in working with lower bounds is invertible extensions. They allow one to turn a lower bound of an operator into the norm of an inverse operator. Some results giving extensions are known for single operators and certain other semigroup representations. Chapter 3 includes some positive new results for operators on Hilbert space and also certain unbounded operators. An example shows that a uniform lower bound for the powers of an operator does not give an extension with power bounded inverse. Variations are given for generators of C0-semigroups, and for operators on Hilbert space. A result by Read, which gives an extension with minimal spectrum raises the question how the lower bounds of the original operator are related to the resolvent bounds of the extension. Another tool which is developed in this thesis is a reduction using semi- norms. A seminorm can place a different emphasis on elements and even neglect some. In this way, we can shape a Banach space to attain properties that we impose. This idea is used to define maximal parts in Chapter 4. They are identified in the context of contractivity and expansiveness of a bounded operator, and in the context of dissipativity and accretivity for certain unbounded operators. Applications are an improvement of a theorem by Batty and Tomilov which characterises embeddings into hyperbolic C0-semigroups, and a generalisation of a theorem by Goldberg and Smith leading to a characterisation of generators of C0-semigroups which have an extending group with bounded inverses.
Subjects/Keywords: 515
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APA (6th Edition):
Geyer, F. (2015). Improving properties of operators by extensions and reductions. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:f2978369-108e-4143-9000-50a11c973e83 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712095
Chicago Manual of Style (16th Edition):
Geyer, Felix. “Improving properties of operators by extensions and reductions.” 2015. Doctoral Dissertation, University of Oxford. Accessed March 01, 2021.
https://ora.ox.ac.uk/objects/uuid:f2978369-108e-4143-9000-50a11c973e83 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712095.
MLA Handbook (7th Edition):
Geyer, Felix. “Improving properties of operators by extensions and reductions.” 2015. Web. 01 Mar 2021.
Vancouver:
Geyer F. Improving properties of operators by extensions and reductions. [Internet] [Doctoral dissertation]. University of Oxford; 2015. [cited 2021 Mar 01].
Available from: https://ora.ox.ac.uk/objects/uuid:f2978369-108e-4143-9000-50a11c973e83 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712095.
Council of Science Editors:
Geyer F. Improving properties of operators by extensions and reductions. [Doctoral Dissertation]. University of Oxford; 2015. Available from: https://ora.ox.ac.uk/objects/uuid:f2978369-108e-4143-9000-50a11c973e83 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712095
University of Exeter
19.
Perryman, Clare Georgina.
How fast is too fast? : rate-induced bifurcations in multiple time-scale systems.
Degree: PhD, 2015, University of Exeter
URL: http://hdl.handle.net/10871/21141
► This thesis studies the phenomena of rate-induced bifurcations. Externally forced systems may have a critical rate, above which they undergo some sort of destabilisation, and…
(more)
▼ This thesis studies the phenomena of rate-induced bifurcations. Externally forced systems may have a critical rate, above which they undergo some sort of destabilisation, and move away suddenly to a new state. Mathematically, the phenomenon is a non-autonomous instability. We present a framework in which rate-induced bifurcations can be studied. This is based on geometric singular perturbation theory which is derived from Fenichel’s Theorem. In particular we make use of folded singularities and canard trajectories, which are modern concepts from geometric singular perturbation theory. We concentrate on systems with multiple time-scales where the mechanism for a rate-induced bifurcation is not obvious. So much so, that once a multiple time-scale system has undergone a rate-induced bifurcation, the instability threshold which separates initial states that destabilise from those that adiabatically follow a changing stable state is described as non-obvious. We study in detail the complicated non-obvious instability threshold that arises near a folded saddle-node (type I) singularity. In particular, we show how the complicated threshold structure depends on two parameters – the ratio of time-scales and the the folded singularity bifurcation parameter. In contrast, we also show single time-scale systems where the rate-induced bifurcation is caused by a large perturbation in the boundary of the basin of attraction for the stable state.
Subjects/Keywords: 515
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APA (6th Edition):
Perryman, C. G. (2015). How fast is too fast? : rate-induced bifurcations in multiple time-scale systems. (Doctoral Dissertation). University of Exeter. Retrieved from http://hdl.handle.net/10871/21141
Chicago Manual of Style (16th Edition):
Perryman, Clare Georgina. “How fast is too fast? : rate-induced bifurcations in multiple time-scale systems.” 2015. Doctoral Dissertation, University of Exeter. Accessed March 01, 2021.
http://hdl.handle.net/10871/21141.
MLA Handbook (7th Edition):
Perryman, Clare Georgina. “How fast is too fast? : rate-induced bifurcations in multiple time-scale systems.” 2015. Web. 01 Mar 2021.
Vancouver:
Perryman CG. How fast is too fast? : rate-induced bifurcations in multiple time-scale systems. [Internet] [Doctoral dissertation]. University of Exeter; 2015. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10871/21141.
Council of Science Editors:
Perryman CG. How fast is too fast? : rate-induced bifurcations in multiple time-scale systems. [Doctoral Dissertation]. University of Exeter; 2015. Available from: http://hdl.handle.net/10871/21141
Durham University
20.
Charlton, Steven Paul.
Identities arising from coproducts on multiple zeta values and multiple polylogarithms.
Degree: PhD, 2016, Durham University
URL: http://etheses.dur.ac.uk/11834/
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.699513
► In this thesis we explore identities which can be proven on multiple zeta values using the derivation operators Dr from Brown's motivic MZV framework. We…
(more)
▼ In this thesis we explore identities which can be proven on multiple zeta values using the derivation operators Dr from Brown's motivic MZV framework. We then explore identities which occur on multiple polylogarithms by way of the symbol map 𝓢 , and the multiple polylogarithm coproduct Δ . On multiple zeta values, we consider Borwein, Bradley, Broadhurst, and Lisoněk's cyclic insertion conjecture about inserting blocks of {2}ai between the arguments of ζ({1,3}n) . We generalise this conjecture to a much broader setting, and give a proof of a symmetrisation of this generalised cyclic insertion conjecture. This proof is by way of the block-decomposition of iterated integrals introduced here, and Brown's motivic MZV framework. This symmetrisation allows us to prove (or to make progress towards) various conjectural identities, including the original cyclic insertion conjecture, and Hoffman's 2ζ(3,3,{2}n) - ζ(3,{2}n,1,2) identity. Moreover, we can then generate unlimited new conjectural identities, and give motivic proofs of their symmetrisations. We then consider the task of relating weight 5 multiple polylogarithms. Using the symbol map, we determine all of the symmetries and functional equations between depth 2 and between depth 3 iterated integrals with 'coupled-cross ratio' arguments [{cr}(a,b,c,d1), …, {cr}(a,b,c,dk)] . We lift the identity for I4,1(x,y) + I4,1(\frac{1}{x}, \frac{1}{y}) to an identity holding exactly on the level of the symbol and prove a generalisation of this for Ia,b(x,y) . Moreover, we further lift the subfamily In,1 to a candidate numerically testable identity using slices of the coproduct. We review Dan's reduction method for reducing the iterated integral I1,1,…,1 to a sum in ≤ n-2 variables. We provide proofs for Dan's claims, and run the method in the case I1,1,1,1 to correct Dan's original reduction of I1,1,1,1 to I3,1 and I4 . We can then compare this with another reduction to find I3,1 functional equations, and their nature. We then give a reduction of I1,1,1,1,1 to I3,1,1 , I3,2 and I5 , and indicate how one might be able to further reduce to I3,2 and I5 . Lastly, we use and generalise an idea suggested by Goncharov at weight 4 and weight 5. We find {Li}n terms when certain {Li}2 , {Li}3 and {Li}4 functional equations are substituted into the arguments of symmetrisations of Im,1(x,y) . By expanding Im,1({{Li}k equation}, {{Li}_ℓ equation}) in two different ways we obtain functional equations for {Li}5 and {Li}6 . We make some suggestions for how this might work at weight 7 and weight 8 giving a potential route to {Li}7 and {Li}8 functional equations.
Subjects/Keywords: 515
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APA (6th Edition):
Charlton, S. P. (2016). Identities arising from coproducts on multiple zeta values and multiple polylogarithms. (Doctoral Dissertation). Durham University. Retrieved from http://etheses.dur.ac.uk/11834/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.699513
Chicago Manual of Style (16th Edition):
Charlton, Steven Paul. “Identities arising from coproducts on multiple zeta values and multiple polylogarithms.” 2016. Doctoral Dissertation, Durham University. Accessed March 01, 2021.
http://etheses.dur.ac.uk/11834/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.699513.
MLA Handbook (7th Edition):
Charlton, Steven Paul. “Identities arising from coproducts on multiple zeta values and multiple polylogarithms.” 2016. Web. 01 Mar 2021.
Vancouver:
Charlton SP. Identities arising from coproducts on multiple zeta values and multiple polylogarithms. [Internet] [Doctoral dissertation]. Durham University; 2016. [cited 2021 Mar 01].
Available from: http://etheses.dur.ac.uk/11834/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.699513.
Council of Science Editors:
Charlton SP. Identities arising from coproducts on multiple zeta values and multiple polylogarithms. [Doctoral Dissertation]. Durham University; 2016. Available from: http://etheses.dur.ac.uk/11834/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.699513
University College London (University of London)
21.
Townsend, A. K.
The mechanics of suspensions.
Degree: PhD, 2017, University College London (University of London)
URL: https://discovery.ucl.ac.uk/id/eprint/1559911/
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724617
► Suspension mechanics—the flow of a fluid with small fragments of solid material suspended in it—is an area of wide applicability in both industry and nature.…
(more)
▼ Suspension mechanics—the flow of a fluid with small fragments of solid material suspended in it—is an area of wide applicability in both industry and nature. Examples include the transport of silt in rivers, the manufacture of toothpaste, and inkjet printing where pigments remain solid within the ink. One widespread method to simulate these flows is Stokesian Dynamics, a truncated multipole expansion of the Stokes equations. It is computationally efficient while making a reasonable approximation to the hydrodynamic interactions between particles; however, all particles are identical spheres and the background matrix must be Newtonian. This project extends Stokesian Dynamics to include differently-sized spheres. This allows us to study a variety of previously inaccessible suspension problems. In many suspensions, e.g. toothpaste, the suspending fluid itself is non-Newtonian and exhibits viscoelastic properties. We have extended Stokesian Dynamics to incorporate a simple model of viscoelasticity by using the small spheres as 'beads' in bead – spring dumbbells. Different spring laws are then tested in shear, and their rheological behaviour is compared to continuum constitutive models. Next, we replicate experiments in which a large sphere is dropped through a suspension of neutrally buoyant smaller spheres undergoing oscillatory shear flow. We qualitatively replicate the principal experimental observation—that at the moment of shear reversal, the suspension microstructure hinders the falling; while at the instant of fastest shear, it enhances the falling. We propose a physical mechanism explaining the observations. Finally, we extend Stokesian Dynamics to properly implement interparticle frictional contact. Contact forces are a critical component of shear thickening in suspensions such as cornflour, yet are usually implemented in an ad hoc way, resulting in inaccurate predictions or high computational cost. The new method allows us to investigate contact models quickly and efficiently, and suggests an important factor in models of strongly shear-thickening fluids.
Subjects/Keywords: 515
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APA (6th Edition):
Townsend, A. K. (2017). The mechanics of suspensions. (Doctoral Dissertation). University College London (University of London). Retrieved from https://discovery.ucl.ac.uk/id/eprint/1559911/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724617
Chicago Manual of Style (16th Edition):
Townsend, A K. “The mechanics of suspensions.” 2017. Doctoral Dissertation, University College London (University of London). Accessed March 01, 2021.
https://discovery.ucl.ac.uk/id/eprint/1559911/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724617.
MLA Handbook (7th Edition):
Townsend, A K. “The mechanics of suspensions.” 2017. Web. 01 Mar 2021.
Vancouver:
Townsend AK. The mechanics of suspensions. [Internet] [Doctoral dissertation]. University College London (University of London); 2017. [cited 2021 Mar 01].
Available from: https://discovery.ucl.ac.uk/id/eprint/1559911/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724617.
Council of Science Editors:
Townsend AK. The mechanics of suspensions. [Doctoral Dissertation]. University College London (University of London); 2017. Available from: https://discovery.ucl.ac.uk/id/eprint/1559911/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.724617
22.
Dempsey, Liam.
Nonlinear exact coherent structures in high Reynolds number shear flows.
Degree: PhD, 2015, Imperial College London
URL: http://hdl.handle.net/10044/1/33319
► Recently a dynamical systems approach to the process of transition to turbulence has arisen in which so called exact coherent structures play a key role.…
(more)
▼ Recently a dynamical systems approach to the process of transition to turbulence has arisen in which so called exact coherent structures play a key role. Such structures are equilibrium states which are exact solutions of the Navier-Stokes equations. Given the nature of the governing equations such states can be difficult to find due to the size of the state space and nonlinear effects. Techniques such as homotopy and artificial forcing have been used to overcome these issues. However, here we will focus on finding such states at large Reynolds numbers where an asymptotically large parameter allows the identification of the leading order effects, from which the structure of the states can be described. The states described in this thesis will be split into two general types. The first are of vortex-Tollmien-Schlichting-wave type and these states arise via the viscous instability mechanism. The flows studied here (plane Poiseuille flow and the asymptotic suction boundary layer) both exhibit a linear instability and hence we can find nonlinear travelling wave equilibrium states which bifurcate directly from the basic state. Importantly the class of states studied here have a large spanwise wavelength. We will find and investigate these states, finding that they appear to terminate in a singularity caused by the lack of spanwise diffusion at leading order. The second type are characterised by the presence of structures both in the freestream and close to the wall, and were first found by Deguchi & Hall (J. Fluid Mech, vol. 752, 2014, pp. 602-625). We will consider two variations of these states. The first is the effect of wall curvature which leads to the imperfect bifurcation of Görtler vortices from the basic state. The second is the spontaneous generation of near wall structures when freestream structures are assumed to appear impulsively at some downstream location.
Subjects/Keywords: 515
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APA ·
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APA (6th Edition):
Dempsey, L. (2015). Nonlinear exact coherent structures in high Reynolds number shear flows. (Doctoral Dissertation). Imperial College London. Retrieved from http://hdl.handle.net/10044/1/33319
Chicago Manual of Style (16th Edition):
Dempsey, Liam. “Nonlinear exact coherent structures in high Reynolds number shear flows.” 2015. Doctoral Dissertation, Imperial College London. Accessed March 01, 2021.
http://hdl.handle.net/10044/1/33319.
MLA Handbook (7th Edition):
Dempsey, Liam. “Nonlinear exact coherent structures in high Reynolds number shear flows.” 2015. Web. 01 Mar 2021.
Vancouver:
Dempsey L. Nonlinear exact coherent structures in high Reynolds number shear flows. [Internet] [Doctoral dissertation]. Imperial College London; 2015. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10044/1/33319.
Council of Science Editors:
Dempsey L. Nonlinear exact coherent structures in high Reynolds number shear flows. [Doctoral Dissertation]. Imperial College London; 2015. Available from: http://hdl.handle.net/10044/1/33319
23.
Jain, Kurunandan.
Leading edge instability and generation of Tollmien-Schlichting waves and wave packets.
Degree: PhD, 2016, Imperial College London
URL: http://hdl.handle.net/10044/1/45306
► This thesis is concerned with the effect that boundary layer instabilities have on laminar-turbulent transition over an aircraft wing. The receptivity analysis of the two-dimensional…
(more)
▼ This thesis is concerned with the effect that boundary layer instabilities have on laminar-turbulent transition over an aircraft wing. The receptivity analysis of the two-dimensional marginal separation flow with respect to suction/blowing is considered. The solution of the linearised perturbation equation is sought in the form of perturbations that are periodic in time. Numerical results are obtained and it is observed that for large enough frequencies Tollmien-Schlicting wave packets begin to form downstream of a source of perturbations. A receptivity analysis of an incompressible steady two-dimensional marginally separated laminar boundary layer with respect to three-dimensional unsteady perturbations is then considered. An asymptotic theory of this flow is constructed on the basis of an analysis of the Navier-Stokes equations at large Reynolds numbers by means of matched asymptotic expansions. Two particular cases are considered, one in which we assume that the solution is periodic in both time T and the spanwise coordinate Z, and the second where the solution is periodic in time only. As a result an integro-differential equation is derived and studied numerically by means of a spectral method. The next mathematical formulation is the study of marginal separation theory for a swept wing. In this formulation, an additional equation for the spanwise velocity component w is needed. Upon solving the triple-deck equations, an algebraic Fourier transform equation is obtained and solved numerically. Finally, the last chapter concerns itself with a numerical global stability of the two-dimensional unsteady marginal separation equation.
Subjects/Keywords: 515
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APA (6th Edition):
Jain, K. (2016). Leading edge instability and generation of Tollmien-Schlichting waves and wave packets. (Doctoral Dissertation). Imperial College London. Retrieved from http://hdl.handle.net/10044/1/45306
Chicago Manual of Style (16th Edition):
Jain, Kurunandan. “Leading edge instability and generation of Tollmien-Schlichting waves and wave packets.” 2016. Doctoral Dissertation, Imperial College London. Accessed March 01, 2021.
http://hdl.handle.net/10044/1/45306.
MLA Handbook (7th Edition):
Jain, Kurunandan. “Leading edge instability and generation of Tollmien-Schlichting waves and wave packets.” 2016. Web. 01 Mar 2021.
Vancouver:
Jain K. Leading edge instability and generation of Tollmien-Schlichting waves and wave packets. [Internet] [Doctoral dissertation]. Imperial College London; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10044/1/45306.
Council of Science Editors:
Jain K. Leading edge instability and generation of Tollmien-Schlichting waves and wave packets. [Doctoral Dissertation]. Imperial College London; 2016. Available from: http://hdl.handle.net/10044/1/45306
24.
Rush, Alexander.
Semiclassical phase-space methods for Hermitian and non-Hermitian quantum dynamics.
Degree: PhD, 2016, Imperial College London
URL: http://hdl.handle.net/10044/1/43536
► In this thesis, we study semiclassical phase-space methods for quantum evolution in Hermitian and non-Hermitian systems. We first present the dynamics of Gaussian wave packets…
(more)
▼ In this thesis, we study semiclassical phase-space methods for quantum evolution in Hermitian and non-Hermitian systems. We first present the dynamics of Gaussian wave packets under non-Hermitian Hamiltonians and interpret them as a classical dynamics for complex Hamiltonians. We use these to derive exact dynamics for wave packets in the quadratic Swanson oscillator. We show that in the case of unbroken PT-symmetry there can be periodic divergences in this system and relate this to the fact that any operator mapping the system to a Hermitian counterpart is unbounded. We apply the semiclassical wave-packet dynamics to two further anharmonic example systems: a PT-symmetric wave guide, a version of which we propose as a filtering device for optical beams, and a non-Hermitian single-band tight-binding model, for which we use classical equations of motion to model both narrowly and widely distributed initial states. We further develop an exact quantum propagator for non-Hermitian dynamics using lattices of wave packets, whose evolution is governed by the semiclassical equations of motion. We demonstrate that this accurately reproduces quantum dynamics compared to the split operator method. Finally we study a Hermitian two-mode many-particle model for bosonic atom-molecule conversion, for which the classical phase-space structure is an orbifold. We show that standard semiclassical tools may be applied to recover features such as the dynamics, spectrum and density of states of the many-particle system.
Subjects/Keywords: 515
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APA ·
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APA (6th Edition):
Rush, A. (2016). Semiclassical phase-space methods for Hermitian and non-Hermitian quantum dynamics. (Doctoral Dissertation). Imperial College London. Retrieved from http://hdl.handle.net/10044/1/43536
Chicago Manual of Style (16th Edition):
Rush, Alexander. “Semiclassical phase-space methods for Hermitian and non-Hermitian quantum dynamics.” 2016. Doctoral Dissertation, Imperial College London. Accessed March 01, 2021.
http://hdl.handle.net/10044/1/43536.
MLA Handbook (7th Edition):
Rush, Alexander. “Semiclassical phase-space methods for Hermitian and non-Hermitian quantum dynamics.” 2016. Web. 01 Mar 2021.
Vancouver:
Rush A. Semiclassical phase-space methods for Hermitian and non-Hermitian quantum dynamics. [Internet] [Doctoral dissertation]. Imperial College London; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10044/1/43536.
Council of Science Editors:
Rush A. Semiclassical phase-space methods for Hermitian and non-Hermitian quantum dynamics. [Doctoral Dissertation]. Imperial College London; 2016. Available from: http://hdl.handle.net/10044/1/43536
25.
Sektnan, Lars Martin.
Poincaré type Kähler metrics and stability on toric varieties.
Degree: PhD, 2016, Imperial College London
URL: http://hdl.handle.net/10044/1/43380
► In this thesis we study the relationship between the existence of extremal Kähler metrics and stability. We introduce a space of symplectic potentials for toric…
(more)
▼ In this thesis we study the relationship between the existence of extremal Kähler metrics and stability. We introduce a space of symplectic potentials for toric manifolds, which we show gives metrics with mixed Poincaré type and cone angle singularities. We show uniqueness and that existence implies stability for extremal metrics arising from these potentials. For quadrilaterals, we give a computable criterion for stability in certain cases, giving a definite log-stable region for generic quadrilaterals. We use computational tools to find new examples of stable and unstable toric manifolds. For Poincaré type manifolds with an S1-action, we prove a version of the LeBrun-Simanca openness theorem and Arezzo-Pacard blow-up theorem.
Subjects/Keywords: 515
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APA (6th Edition):
Sektnan, L. M. (2016). Poincaré type Kähler metrics and stability on toric varieties. (Doctoral Dissertation). Imperial College London. Retrieved from http://hdl.handle.net/10044/1/43380
Chicago Manual of Style (16th Edition):
Sektnan, Lars Martin. “Poincaré type Kähler metrics and stability on toric varieties.” 2016. Doctoral Dissertation, Imperial College London. Accessed March 01, 2021.
http://hdl.handle.net/10044/1/43380.
MLA Handbook (7th Edition):
Sektnan, Lars Martin. “Poincaré type Kähler metrics and stability on toric varieties.” 2016. Web. 01 Mar 2021.
Vancouver:
Sektnan LM. Poincaré type Kähler metrics and stability on toric varieties. [Internet] [Doctoral dissertation]. Imperial College London; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10044/1/43380.
Council of Science Editors:
Sektnan LM. Poincaré type Kähler metrics and stability on toric varieties. [Doctoral Dissertation]. Imperial College London; 2016. Available from: http://hdl.handle.net/10044/1/43380
University of Sheffield
26.
Fuller, Benjamin James.
Skew monoidal categories and Grothendieck's six operations.
Degree: PhD, 2017, University of Sheffield
URL: http://etheses.whiterose.ac.uk/16499/
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706055
► In this thesis, we explore several topics in the theory of monoidal and skew monoidal categories. In Chapter 3, we give definitions of dual pairs…
(more)
▼ In this thesis, we explore several topics in the theory of monoidal and skew monoidal categories. In Chapter 3, we give definitions of dual pairs in monoidal categories, skew monoidal categories, closed skew monoidal categories and closed monoidal categories. In the case of monoidal and closed monoidal categories, there are multiple well-known definitions of a dual pair. We generalise these definitions to skew monoidal and closed skew monoidal categories. In Chapter 4, we introduce semidirect products of skew monoidal categories. Semidirect products of groups are a well-known and well-studied algebraic construction. Semidirect products of monoids can be defined analogously. We provide a categorification of this construction, for semidirect products of skew monoidal categories. We then discuss semidirect products of monoidal, closed skew monoidal and closed monoidal categories, in each case providing sufficient conditions for the semidirect product of two skew monoidal categories with the given structure to inherit the structure itself. In Chapter 5, we prove a coherence theorem for monoidal adjunctions between closed monoidal categories, a fragment of Grothendieck's 'six operations' formalism.
Subjects/Keywords: 515
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APA (6th Edition):
Fuller, B. J. (2017). Skew monoidal categories and Grothendieck's six operations. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/16499/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706055
Chicago Manual of Style (16th Edition):
Fuller, Benjamin James. “Skew monoidal categories and Grothendieck's six operations.” 2017. Doctoral Dissertation, University of Sheffield. Accessed March 01, 2021.
http://etheses.whiterose.ac.uk/16499/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706055.
MLA Handbook (7th Edition):
Fuller, Benjamin James. “Skew monoidal categories and Grothendieck's six operations.” 2017. Web. 01 Mar 2021.
Vancouver:
Fuller BJ. Skew monoidal categories and Grothendieck's six operations. [Internet] [Doctoral dissertation]. University of Sheffield; 2017. [cited 2021 Mar 01].
Available from: http://etheses.whiterose.ac.uk/16499/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706055.
Council of Science Editors:
Fuller BJ. Skew monoidal categories and Grothendieck's six operations. [Doctoral Dissertation]. University of Sheffield; 2017. Available from: http://etheses.whiterose.ac.uk/16499/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706055
University of Sheffield
27.
O'Sullivan, David Robert.
Topological C*-categories.
Degree: PhD, 2017, University of Sheffield
URL: http://etheses.whiterose.ac.uk/16775/
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707474
► Tensor C*-categories are the result of work to recast the fundamental theory of operator algebras in the setting of category theory, in order to facilitate…
(more)
▼ Tensor C*-categories are the result of work to recast the fundamental theory of operator algebras in the setting of category theory, in order to facilitate the study of higher-dimensional algebras that are expected to play an important role in a unified model of physics. Indeed, the application of category theory to mathematical physics is itself a highly active field of research. C*-categories are the analogue of C*-algebras in this context. They are defined as norm-closed self-adjoint subcategories of the category of Hilbert spaces and bounded linear operators between them. Much of the theory of C*-algebras and their invariants generalises to C*-categories. Often, when a C*-algebra is associated to a particular structure it is not completely natural because certain choices are involved in its definition. Using C*-categories instead can avoid such choices since the construction of the relevant C*-category amounts to choosing all suitable C*-algebras at once. In this thesis we introduce and study C*-categories for which the set of objects carries topological data, extending the present body of work, which exclusively considers C*-categories with discrete object sets. We provide a construction of K-theory for topological C*-categories, which will have applications in widening the scope of the Baum-Connes conjecture, in index theory, and in geometric quantisation. As examples of such applications, we construct the C*-categories of topological groupoids, extending the familiar constructions of Renault.
Subjects/Keywords: 515
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APA ·
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MLA ·
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to Zotero / EndNote / Reference
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APA (6th Edition):
O'Sullivan, D. R. (2017). Topological C*-categories. (Doctoral Dissertation). University of Sheffield. Retrieved from http://etheses.whiterose.ac.uk/16775/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707474
Chicago Manual of Style (16th Edition):
O'Sullivan, David Robert. “Topological C*-categories.” 2017. Doctoral Dissertation, University of Sheffield. Accessed March 01, 2021.
http://etheses.whiterose.ac.uk/16775/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707474.
MLA Handbook (7th Edition):
O'Sullivan, David Robert. “Topological C*-categories.” 2017. Web. 01 Mar 2021.
Vancouver:
O'Sullivan DR. Topological C*-categories. [Internet] [Doctoral dissertation]. University of Sheffield; 2017. [cited 2021 Mar 01].
Available from: http://etheses.whiterose.ac.uk/16775/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707474.
Council of Science Editors:
O'Sullivan DR. Topological C*-categories. [Doctoral Dissertation]. University of Sheffield; 2017. Available from: http://etheses.whiterose.ac.uk/16775/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707474
University of Surrey
28.
Pennant, Jonathan P.
On infinite energy solutions to dissipative PDEs in unbounded domains.
Degree: PhD, 2016, University of Surrey
URL: http://epubs.surrey.ac.uk/810980/
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690411
► In this thesis several problems in Partial Differential Equations in unbounded domains are studied using the techniques of uniformly local spaces and weighted energy theory.…
(more)
▼ In this thesis several problems in Partial Differential Equations in unbounded domains are studied using the techniques of uniformly local spaces and weighted energy theory. First Coupled Burger's equations are studied on the whole space R and existence of solutions in uniformly local spaces is proven in the case where the non-linearity is gradient. Moreover the uniqueness of these solutions and some additional regularity is proven. Second the Cahn-Hilliard, and closely related Cahn-Hilliard-Oono, equations are studied on the whole space R3 with both polynomial and singular potentials and existence of solutions in uniformly local spaces is proven. Moreover uniqueness and additional regularity of these equations is also proven. Third the Navier-Stokes equations are studied on the whole space R2 and, building on the work of Zelik who showed the existence of solutions in uniformly local spaces, the existence of a finite dimensional globally compact attractor is proven in the case where the forcing term has arbitrarily slow decay at infinity.
Subjects/Keywords: 515
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APA (6th Edition):
Pennant, J. P. (2016). On infinite energy solutions to dissipative PDEs in unbounded domains. (Doctoral Dissertation). University of Surrey. Retrieved from http://epubs.surrey.ac.uk/810980/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690411
Chicago Manual of Style (16th Edition):
Pennant, Jonathan P. “On infinite energy solutions to dissipative PDEs in unbounded domains.” 2016. Doctoral Dissertation, University of Surrey. Accessed March 01, 2021.
http://epubs.surrey.ac.uk/810980/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690411.
MLA Handbook (7th Edition):
Pennant, Jonathan P. “On infinite energy solutions to dissipative PDEs in unbounded domains.” 2016. Web. 01 Mar 2021.
Vancouver:
Pennant JP. On infinite energy solutions to dissipative PDEs in unbounded domains. [Internet] [Doctoral dissertation]. University of Surrey; 2016. [cited 2021 Mar 01].
Available from: http://epubs.surrey.ac.uk/810980/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690411.
Council of Science Editors:
Pennant JP. On infinite energy solutions to dissipative PDEs in unbounded domains. [Doctoral Dissertation]. University of Surrey; 2016. Available from: http://epubs.surrey.ac.uk/810980/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.690411
University of Leeds
29.
Bin-Mohsin, Bandar Abdullah.
The method of fundamental solutions for Helmholtz-type problems.
Degree: PhD, 2013, University of Leeds
URL: http://etheses.whiterose.ac.uk/4843/
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.589233
► The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems…
(more)
▼ The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems associated with two- or three-dimensional Helmholtz-type equations. Inverse problems have become more and more important in various fields of science and technology, and have certainly been one of the fastest growing areas in applied mathematics over the last three decades. However, as inverse geometric problems typically lead to mathematical models which are ill-posed, their solutions are unstable under data perturbations and classical numerical techniques fail to provide accurate and stable solutions.
Subjects/Keywords: 515
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Record Details
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APA ·
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MLA ·
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Export
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APA (6th Edition):
Bin-Mohsin, B. A. (2013). The method of fundamental solutions for Helmholtz-type problems. (Doctoral Dissertation). University of Leeds. Retrieved from http://etheses.whiterose.ac.uk/4843/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.589233
Chicago Manual of Style (16th Edition):
Bin-Mohsin, Bandar Abdullah. “The method of fundamental solutions for Helmholtz-type problems.” 2013. Doctoral Dissertation, University of Leeds. Accessed March 01, 2021.
http://etheses.whiterose.ac.uk/4843/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.589233.
MLA Handbook (7th Edition):
Bin-Mohsin, Bandar Abdullah. “The method of fundamental solutions for Helmholtz-type problems.” 2013. Web. 01 Mar 2021.
Vancouver:
Bin-Mohsin BA. The method of fundamental solutions for Helmholtz-type problems. [Internet] [Doctoral dissertation]. University of Leeds; 2013. [cited 2021 Mar 01].
Available from: http://etheses.whiterose.ac.uk/4843/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.589233.
Council of Science Editors:
Bin-Mohsin BA. The method of fundamental solutions for Helmholtz-type problems. [Doctoral Dissertation]. University of Leeds; 2013. Available from: http://etheses.whiterose.ac.uk/4843/ ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.589233
30.
Garcia Ramirez, Erick.
Non-archimedean stratifications in T-convex fields.
Degree: PhD, 2017, University of Leeds
URL: http://etheses.whiterose.ac.uk/18362/
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.725009
► We prove that whenever T is a power-bounded o-minimal theory, t-stratifications exist for definable maps and sets in T-convex fields. To this effect, a thorough…
(more)
▼ We prove that whenever T is a power-bounded o-minimal theory, t-stratifications exist for definable maps and sets in T-convex fields. To this effect, a thorough analysis of definability in T-convex fields is carried out. One of the conditions required for the result above is the Jacobian property, whose proof in this work is a long and technical argument based on an earlier proof of this property for valued fields with analytic structure. An example is given to illustrate that t-stratifications do not exist in general when T is not power-bounded. We also show that if T is power-bounded, the theory of all T-convex fields is b-minimal with centres. We also address several applications of tstratifications. For this we exclusively work with a power-bounded T. The first application establishes that a t-stratification of a definable set X in a T-convex field induces t stratifications on the tangent cones of X. This is a contribution to local geometry and singularity theory. Regarding R as a model of T, the remaining applications are derived by considering the stratifications induced on R by t-stratifications in non-standard models. We prove that each such induced stratification is a C1-Whitney stratification; this in turn leads to a new proof of the existence of Whitney stratifications for definable sets in R. We also deal with interactions between tangent cones of definable sets in R and stratifications.
Subjects/Keywords: 515
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APA ·
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MLA ·
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CSE |
Export
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APA (6th Edition):
Garcia Ramirez, E. (2017). Non-archimedean stratifications in T-convex fields. (Doctoral Dissertation). University of Leeds. Retrieved from http://etheses.whiterose.ac.uk/18362/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.725009
Chicago Manual of Style (16th Edition):
Garcia Ramirez, Erick. “Non-archimedean stratifications in T-convex fields.” 2017. Doctoral Dissertation, University of Leeds. Accessed March 01, 2021.
http://etheses.whiterose.ac.uk/18362/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.725009.
MLA Handbook (7th Edition):
Garcia Ramirez, Erick. “Non-archimedean stratifications in T-convex fields.” 2017. Web. 01 Mar 2021.
Vancouver:
Garcia Ramirez E. Non-archimedean stratifications in T-convex fields. [Internet] [Doctoral dissertation]. University of Leeds; 2017. [cited 2021 Mar 01].
Available from: http://etheses.whiterose.ac.uk/18362/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.725009.
Council of Science Editors:
Garcia Ramirez E. Non-archimedean stratifications in T-convex fields. [Doctoral Dissertation]. University of Leeds; 2017. Available from: http://etheses.whiterose.ac.uk/18362/ ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.725009
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Open Access Theses and Dissertations
