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.


== Cosica 1 ==
== Topology of flows ==


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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.


== Cosica 2 ==
== Non-diffusive transport ==


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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).


== Cosica 3 ==
== 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 ==
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