Related papers: A Ritz variational principle for local collisionle…
It is tempting to raise the issue of (metric) chaos in general relativity since the Einstein equations are a set of highly nonlinear equations which may exhibit dynamically very complicated solutions for the space-time metric. However, in…
We develop a new robust technique to deduce variance principles for non-integrable discrete systems. To illustrate this technique, we show the existence of a variational principle for graph homomorphisms from $\Z^m$ to a $d$-regular tree.…
We present a systematic derivation of a model based on the central moment lattice Boltzmann equation that rigorously maintains Galilean invariance of forces to simulate inertial frame independent flow fields. In this regard, the central…
The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order $o(\bar{g})$ in the coupling constant $\bar{g}$. As a first application, based on the Riemann-Liouville…
Upper bounds on the growth of free energy in gyrokinetics are derived. These bounds apply to all local gyrokinetic instabilities in the geometry of a flux tube, i.e. a slender volume of plasma aligned with the magnetic field, regardless of…
Based on the requirement of covariance, we propose a new approach for generalizing fractional calculus in multi-dimensional space. As a first application we calculate an approximation for the ground state energy of the fractional…
The identification of stream in the straight pipe as a flexible rod has allowed to present the criterion expression for determination of transition of the laminar flow regime to the turbulent as a loss of stability of the rectilinear static…
A crucial issue in relativistic plasma, particularly relevant in the astrophysical context, is the description of highly magnetized plasmas based on a covariant formulation of gyrokinetic dynamics. An interesting case in question is that in…
We perform a local stability analysis of rotational flows in the presence of a constant vertical magnetic field and an azimuthal magnetic field with a general radial dependence. Employing the short-wavelength approximation we develop a…
Gyrokinetic theory is based on an asymptotic expansion in the small parameter $\epsilon$, defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this article, this ordering is strictly…
This dissertation is about the study of three important issues in the theory of relativistic fluid dynamics: the stability of dissipative fluid dynamics, the shear viscosity, and fluid dynamics with triangle anomaly.(1)The second order…
Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent…
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,…
We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of…
Microinstabilities drive turbulent fluctuations in inhomogeneous, magnetized plasmas. In the context of magnetic confinement fusion devices, this leads to an enhanced transport of particles, momentum, and energy, thereby degrading…
Starting from the equations of collisionless linear gyrokinetics for magnetised plasmas with an imposed inhomogeneous magnetic field, we present the first known analytical, closed-form solution for the resulting velocity-space integrals in…
We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational…
We construct a description of Ion Temperature Gradient (ITG) driven localised linear modes which retains both wave-particle and magnetic drift resonant effects while capturing the field-line dependence of the electrostatic potential. We…
Thermal and other transport coefficients were recently shown to be largely independent of the microscopic representation of the energy (current) densities or, more generally, of the relevant conserved densities/currents. In this paper we…
Axisymmetric ($m=0$) gyrokinetic and extended-MHD simulations of sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic…