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Topological characteristics reveal important physical properties of plasma structures and astrophysical processes. Physical parameters and constraints are linked with topological invariants, which are important for describing magnetic…
In our Solar system, spin-orbit resonances are common under Sun--planet, planet--satellite and binary asteroid configurations. In this work, high-order and secondary spin-orbit resonances are investigated by taking numerical and analytical…
In general, small bodies of the solar system, e.g., asteroids and comets, have a very irregular shape. This feature affects significantly the gravitational potential around these irregular bodies, which hinders dynamical studies. The…
Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined…
Classical beams of light with non-uniform polarization patterns (e.g. radially and azimuthally polarized doughnut beams) may exhibit quantum-like features as, for instance, inseparability. We establish an exact correspondence between…
Although tokamaks are one of the most promising devices for realizing nuclear fusion as an energy source, there are still key obstacles when it comes to understanding the dynamics of the plasma and controlling it. As such, it is crucial…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
Machine learning is applied to investigate the phase transition of two-dimensional complex plasmas. The Langevin dynamics simulation is employed to prepare particle suspensions in various thermodynamic states. Based on the resulted particle…
The effects of resonant magnetic perturbations on the turbulent transport of fast ions in tokamak devices are investigated using a theoretical transport model of test-particle type. The direct numerical simulation method is used to compute,…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
Autonomous terrain classification is an important problem in planetary navigation, whether the goal is to identify scientific sites of interest or to traverse treacherous areas safely. Past Martian rovers have relied on human operators to…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…
The Product of Exponentials (PoE) formula is a mathematical tool that is used extensively in robotics. The virtue of using the exponential mapping, Lie Algebra and screw theory is that it allows an elegant and concise way of describing the…
Modern Tokamaks have evolved from the initial axisymmetric circular plasma shape to an elongated axisymmetric plasma shape that improves the energy confinement time and the triple product, which is a generally used figure of merit for the…
The penalization method is used to take account of obstacles in a tokamak, such as the limiter. We study a non linear hyperbolic system modelling the plasma transport in the area close to the wall. A penalization which cuts the transport…
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar\'e equations on Lie groups and homogeneous spaces. Orbit…
Grid decarbonization for climate change requires dispatchable carbon-free energy like nuclear fusion. The tokamak concept offers a promising path for fusion, but one of the foremost challenges in implementation is the occurrence of…
Compact formulas for trapped-particle and passing-particle guiding-center orbits in axisymmetric tokamak geometry are given in terms of the Jacobi elliptic functions and complete elliptic integrals. These formulas can find applications in…
The Tokamak device is the most promising candidate for producing sustainable electric power by nuclear fusion. It is a torus-shaped device that confines plasma by a strong magnetic field. The development, design and control of the design…