Related papers: Global Sensitivity Analysis of Plasma Instabilitie…
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…
We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy…
An analysis of plasma density distributions at arbitrary ion-atom collisionality for one-dimensional axially symmetrical cylindrical and annular plasmas is presented. Perturbations of plasma densities caused by a cylindrical probe are…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
Panel data allows for the modeling of unobserved heterogeneity, significantly raising the number of nuisance parameters and making high dimensionality a practical issue. Meanwhile, temporal and cross-sectional dependence in panel data…
We propose an uncertainty propagation study and a sensitivity analysis with the Ocular Mathematical Virtual Simulator, a computational and mathematical model that predicts the hemodynamics and biomechanics within the human eye. In this…
We present an approach to analyze $C^1(\mathbb{R}^m)$ functions that addresses limitations present in the Active Subspaces (AS) method of Constantine et al.(2015; 2014). Under appropriate hypotheses, our Active Manifolds (AM) method…
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a novel approach using periodic orbit theory to analyze plasma turbulence, identifying fundamental structures…
A generalized hydrodynamic (GHD) model depicting the behaviour of visco-elastic fluids has often been invoked to explore the behaviour of a strongly coupled dusty plasma medium below their crystallization limit. The model has been…
A uniform in space, oscillatory in time plasma equilibrium sustained by a time-dependent current density is analytically and numerically studied resorting to particle-in-cell simulations. The dispersion relation is derived from the Vlasov…
Stabilizing plasma dynamics is a central challenge in magnetic confinement fusion. A common approach is to introduce external electric fields to suppress instabilities in the plasma distribution. However, efficiently identifying such…
Rayleigh-Taylor and Buoyancy-driven instabilities are very common instabilities for an inhomogeneous medium. We examine here how these instabilities grow for incompressible viscoelastic fluids like a strongly coupled dusty plasma by using…
These lecture notes introduce analytical tools, methods and results describing the growth of cosmological structure beyond the linear regime. The presentation is focused on the single flow regime of the Vlasov-Poisson equation describing…
We consider the plasma confined in a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, and look at a certain class of equilibria, assuming axisymmetry in the problem. We prove a sharp…
We investigate the linear tearing instability in weakly collisional plasmas using a non-ideal gyrotropic-MHD framework, uncovering a previously unknown scaling relation for the instability growth rate in high-$\beta$ environments. Even…
Collisionless, turbulent plasmas surround the Earth, from the magnetosphere to the intergalactic medium, and the fluctuations within them affect nearly every field in the space sciences, from space weather forecasts to theories of galaxy…
We present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of \textit{mutually…
The edge density and temperature of tokamak plasmas are strongly correlated with energy and particle confinement and their quantification is fundamental to understanding edge dynamics. These quantities exhibit behaviours ranging from sharp…
A careful study of plasma-material interactions is essential to understand and improve the operation of devices where plasma contacts a wall. Key contributions of this work include (i) novel continuum kinetic algorithms with novel boundary…
A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for…