Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 91 for “"integrability"”.
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Integrability from Chern-Simons theories
This thesis details my work exploring connections between integrable systems and Chern-Simons theories. It is divided into two parts. The first concerns the application of 4d Chern-Simons theory to describe integrable models with boundary, while the second concerns relations between holomorphic …
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Integrability in random conformal geometry
Liouville quantum gravity (LQG) is a random surface arising as the scaling limit of random planar maps. Schramm-Loewner evolution (SLE) is a random planar curve describing the scaling limits of interfaces in many statistical physics models. Liouville conformal field theory (LCFT) is the quantum …
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Open strings and analytic non-integrability
… theory instead. Based on this concept the integrability, or rather non-integrability of a gauge theory system can be determined using semi-classical string solutions. Integrability has become a coveted property in a system. It indicates that the system can be solved fully. Since there is no …
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Vortices, Painlevé integrability and projective geometry
… in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the …
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Complete integrability and geometrically induced representations
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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Advancing integrability for strings in AdS3/CFT2
In this thesis we develop techniques of integrability in the study of dualities between two-dimensional conformal field theories and theories of closed strings on three-dimensional Anti-de Sitter background geometries. For several years after integrability was first applied to the 3d/2d dualities, …
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A study of integrability conditions for irrotational dust spacetimes
… waves interacting with matter), both imply integrability conditions in the exact non-linear case. The integrability conditions for the divergence-free magnetic Weyl tensor are identically satisfied in the linearized perturbation case, but are non-trivial in the exact non-linear case. This …
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Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field
… and unstable manifolds and the loss of complete integrability. Consequently, the system admits spatially chaotic solutions and a multiplicity of multimodal homoclinic solutions exist. Poincare sections associated with the loss of integrability are displayed. Homoclinic solutions are computed and …
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On the Integrability of Derivatives of Holomorphic and M-Subharmonic Inner Functions In the Unit Ball of Cn
<p>Let Bn be the unit ball in Cn. If f is a bounded holomorphic function, we say that f is inner provided that its modulus has a radial limit of 1 almost everywhere on Sn where Sn is the unit sphere.</p> <p>If a > -1 and p > 0 then Apa denotes the weighted Bergman space of all holomorphic functions …
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Regularity theory for nonlocal equations
… it is only possible to obtain higher integrability, in our nonlocal setting we are able to also prove a substantial amount of higher differentiability. Therefore, our results are in some sense of purely nonlocal type, following a recent trend of such results in the literature.<br /><br …
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Jet groupoids, natural bundles and the Vessiot equivalence method
… thesis, the known methods are extended to check integrability. Furthermore it is shown how to complete the equations to an integrable system efficiently. In all steps, natural bundles are used. For the description of partial differential equations, a geometric approach of Spencer is used. It …
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Searching for self-duality in non-maximally supersymmetric backgrounds
… are of great interest due to their link to integrability. Fermionic T-duality has played a pivotal role in proving that the maximally supersymmetric background AdS₅ × S⁵ is self-dual. This background is also known to be integrable, therefore, when it was shown to be self-dual, the hypothesis …
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Some problems in the dynamics of spatially extended systems
… sine-Gordon equation and the ""Painleve test of integrability."" We present results of our numerical studies of the d.c. driven, damped sine-Gordon equation. We also present a nonperturbative proof of the persistence of soliton-like (""soliton"") and antisoliton-like (""antisoliton"") solutions …
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Lebesgue ▼-Measure and Riemann ▼-Integration
… the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a …
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EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS
… Sobolev-Hilbert H-space, as it only needs square integrability of the gradients of the functions involved. Our results generalize exactly certain well-known results on Laplace's spherical harmonics in classical mathematical physics.
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Rational matrix differential operators and integrable systems of PDEs
A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite hierarchy of generalized symmetries. Recall that V carries a Lie algebra …
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On extended supersymmetry in two and four dimensions.
… aspects. On they way we use various methods of integrability, conformal filed theories and string theory to achieve our goals. We start with describing physics of two dimensional N = 2 sigma models, geometry of their target spaces, their BPS spectra, and how they can de derived from four …
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Equivariant Deformations of Horospherical Surfaces
… indicate how the Goursat transformation law and integrability conditions for the "spin curve" of a horospherical surface are analogous to the Lorentz transformation law and equations of motion for the wavefunction of a massless fermion.
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On Inflationary cosmological models
… do not find exact solutions because of the non-integrability of the field equations, but we can investigate their global properties (and hence their stability) by means of methods of the theory of dynamical systems.
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Integrable symmetric fields in computational design : from stable woven shells to seamless parameterizations
… formulation of an exact formulation of discrete integrability which extends to symmetric frame fields in volumes. The key insight of our work was the introduction of a new "mixed-moment" representation for symmetric frames to the geometry processing literature. We prove that this representation …
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