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Topology and transport: Difference between revisions
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objectives in each of the aforementioned research lines, as well as progress made to date. | objectives in each of the aforementioned research lines, as well as progress made to date. | ||
== | == Topology of flows == | ||
Our long-term aim is to develop a set of diagnostics to characterize the | |||
topological structures in fluid and particle models of a turbulent plasma. In the frame of this project, | |||
and during the next three years, we plan to study the problem in pressure-gradient-driven turbulence, | |||
with a possible extension to gyrokinetic models. For this we will make use of Computational | |||
Homology. An important tool will be the software developed by the Computational Homology Project | |||
(CHomP, see http://chomp.rutgers.edu) which, in particular, computes some topological invariants | |||
(the Betti numbers) of three-dimensional spaces. We will investigate the possibility of developing or | |||
using other tools which allow to improve the numerical resolution of the calculations. | |||
== | == Non-diffusive transport == | ||
Turbulent flows induce non-collisional transport in plasmas. The | |||
final goal is to understand in a precise way the origin and implications of the non-Gaussian and non- | |||
Markovian character of transport in certain dynamical and topological conditions of those turbulent | |||
flows. We will try to make progress in the answer to questions such as: a) The relationship between | |||
the topology of flows and the presence of non-diffusive transport. b) The connection between the | |||
statistical properties of turbulence and the description by means of stochastic and kinetic equations of | |||
particle transport. c) Find out whether there exists a mathematical framework in which one can derive | |||
linear, fractional diffusion equations (in particular non-local) from non-linear, partial differential | |||
equations (in particular local). | |||
== | == Transitions to improved confinement regimes == | ||
The generation of global flows allows to | |||
have regimes with enhanced confinement. We will study the importance of the interaction between | |||
disparate spatio-temporal scales in the generation of sheared flows and the concomitant turbulence | |||
reduction. Our work will be based on recent experimental results in TJ-II. We will use topological | |||
techniques in phase space to gain insight into the dynamics of models with multiple states. | |||
== Cosica 4 == | == Cosica 4 == | ||