Related papers: Fourier-Hankel/Bessel space absolute equilibria of…
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69…
The long-time relaxation of ideal two dimensional magnetohydrodynamic turbulence subject to the conservation of two infinite families of constants of motion---the magnetic and the "cross" topology invariants--is examined. The analysis of…
We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to $4096^2$, for which several quadratic invariants are preserved by the truncation and…
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in…
Electrostatic gyrokinetic absolute equilibria with continuum velocity field are obtained through the partition function and through the Green function of the functional integral. The new results justify and explain the prescription for…
The inviscid, partial differential equations of hydrodynamics when projected via a Galerkin-truncation on a finite-dimensional subspace spanning wavenumbers $-{\bf K}_{\rm G} \le {\bf k} \le {\bf K}_{\rm G}$, and hence retaining a finite…
Two-dimensional gyrokinetics is a simple paradigm for the study of kinetic magnetised plasma turbulence. In this paper, we present a comprehensive theoretical framework for this turbulence. We study both the inverse and direct cascades (the…
The properties of decaying turbulence is studied with the help of a Generalized Hydrodynamic (GHD) fluid model in the context of two dimensional visco - elastic medium such as a strongly coupled dusty plasma system. For the incompressible…
3D2V continuum gyrokinetic simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using the full-$f$ discontinuous-Galerkin code Gkeyll. These simulations include the basic elements of a…
We present a generalised geometry framework for systematically constructing consistent truncations of ten- and eleven-dimensional supergravity preserving varying fractions of supersymmetry. Truncations arise when there is a reduced…
It is shown that the use of a high power $\alpha$ of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid \textit{conservative} dynamics with a finite range of spatial Fourier modes.…
A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent…
We prove a strong Frankel theorem for mean curvature flow shrinkers in all dimensions: Any two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must be connected in all large balls. The key to the…
It is often asserted or implicitly assumed, without justification, that the results of two-dimensional investigations of plasma turbulence are applicable to the three-dimensional plasma environments of interest. A projection method is…
The long-time solutions of the Galerkin-truncated three-dimensional, incompressible Euler equation relax to an absolute equilibrium as a consequence of phase space and kinetic energy conservation in such a finite-dimensional system. These…
In gyrokinetic theory there are two quadratic measures of fluctuation energy, left invariant under nonlinear interactions, that constrain the turbulence. The recent work of Plunk and Tatsuno [Phys. Rev. Lett. 106, 165003 (2011)] reported on…
Effects of quasi-point vortices on the inertial range of scales in homogeneous two-dimensional turbulence (classic and quantum) have been studied using the notion of distributed chaos. Results of direct numerical simulations of decaying…
The linear gyrokinetic stability properties of magnetically confined electron-positron plasmas are investigated in the parameter regime most likely to be relevant for the first laboratory experiments involving such plasmas, where the…
For a magnetised plasma in a straight magnetic guide field, we derive a set of four-dimensional kinetic equations, which can capture electromagnetic turbulence in the drift kinetic limit. To do so, we start from the gyrokinetic equations,…
Electrostatic structures have been observed in many regions of space plasmas, including the solar wind, the magnetosphere, the auroral acceleration region, and in association with shocks, turbulence, and magnetic reconnection. Due to…