Sökning: "Symplectic structure"

Visar resultat 1 - 5 av 9 avhandlingar innehållade orden Symplectic structure.

1. 1. Symplectic methods for isospectral flows and 2D ideal hydrodynamics

   Författare :Milo Viviani; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; NATURVETENSKAP; NATURAL SCIENCES; Symplectic methods; Fluid dynamics; Integrability theory; Euler equations; Lie--Possion systems; Isospectral flows; Geometric integration; Structure preserving algorithms; Hamiltonian systems;

   Sammanfattning : The numerical solution of non-canonical Hamiltonian systems is an active and still growing field of research. At the present time, the biggest challenges concern the realization of structure preserving algorithms for differential equations on infinite dimensional manifolds. LÄS MER

3. 2. Cohomology of the moduli space of curves of genus three with level two structure

   Författare :Olof Bergvall; Carel Faber; Jonas Bergström; Johannes Nicaise; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Algebraic geometry; Moduli space; Cohomology; Symplectic structure; Point count; Mathematics; matematik;

   Sammanfattning : In this thesis we investigate the moduli space M3[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M3[2] into a disjoint union of two natural subspaces, Q[2] and H3[2], and then making S7- resp. LÄS MER

4. 3. Symplectic methods for Hamiltonian isospectral flows and 2D incompressible Euler equations on a sphere

   Författare :Milo Viviani; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Fluid dynamics; Symplectic methods; Isospectral flows; Geometric integration; Hamiltonian systems; Structure preserving algorithms; Euler equations; Lie–Possion systems; Fluid dynamics.;

   Sammanfattning : The numerical solution of non-canonical Hamiltonian systems is an active and still growing field of research. At the present time, the biggest challenges concern the realization of structure preserving algorithms for differential equations on infinite dimensional manifolds. Several classical PDEs can indeed be set in this framework. LÄS MER

5. 4. Geometric discretization for incompressible magnetohydrodynamics on the sphere

   Författare :Michael Roop; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Lie-Poisson structure; magnetohydrodynamics; Hamiltonian dynamics; magnetic extension; Casimirs; symplectic Runge-Kutta integrators;

   Sammanfattning : Many physical processes are modelled by partial differential equations (PDE), and their efficient discretization is still a challenging problem and an actively developing field. An important class of models arising in mathematical physics represents PDEs formulated in terms of a Lie-Poisson structure on the dual of infinite-dimensional Lie algebras, such as the Lie algebra of vector fields. LÄS MER

7. 5. Cohomology of arrangements and moduli spaces

   Författare :Olof Bergvall; Carel Faber; Jonas Bergström; Orsola Tommasi; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Algebraic geometry; moduli spaces; cohomology; toric arrangements; equivariant; point counts; finite fields; mixed Hodge structures; Mathematics; matematik;

   Sammanfattning : This thesis mainly concerns the cohomology of the moduli spaces ℳ3[2] and ℳ3,1[2] of genus 3 curves with level 2 structure without respectively with a marked point and some of their natural subspaces. A genus 3 curve which is not hyperelliptic can be realized as a plane quartic and the moduli spaces ?[2] and ?1[2] of plane quartics without respectively with a marked point are given special attention. LÄS MER