Related papers: Stiff dynamics of electromagnetic two-body motion
The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…
We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…
The parameterised post-Newtonian (PPN) formalism is a weak-field slow-motion approximation for both GR and some of its generalisations. It permits various parameterisations of the motion, among which are the Lagrange-type and Gauss-type…
We perform the asymptotic analysis of parabolic equations with stiff transport terms. This kind of problem occurs, for example, in collisional gyrokinetic theory for tokamak plasmas, where the velocity diffusion of the collision mechanism…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
This paper presents our investigation into the modification of a finite-width internal gravity wave beam arising from triadic resonance instability. We present both experimental and weakly non-linear modelling to examine this instability…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
Upper bounds on the growth of instabilities in gyrokinetic systems have recently been derived by considering the optimal perturbations that maximise the growth of a chosen energy norm. This technique has previously been applied to…
By extracting unstable invariant solutions directly from body-forced three-dimensional turbulence, we study the dynamical processes at play when the forcing is large scale and either unidirectional in the momentum or the vorticity…
We construct and simulate the dynamics of gauged vortons - circular loops of cosmic string supported by the angular momentum of trapped charge and current and provide additional details on the fully stable vorton that we have previously…
We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove…
We study numerically the dynamical system of a two-electron atom with the Darwin interaction as a model to investigate scale-dependent effects of the relativistic action-at-a-distance electrodynamics. This dynamical system consists of a…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
The ongoing energy transition challenges the stability of the electrical power system. Stable operation of the electrical power grid requires both the voltage (amplitude) and the frequency to stay within operational bounds. While much…
We study how the neutron-star equation of state affects the onset of the dynamical instability in the equations of motion for inspiraling neutron-star binaries near coalescence. A combination of relativistic effects and Newtonian tidal…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
Small-scale turbulence originating from microinstabilities limits the energy confinement time in magnetic confinement fusion. Here we develop a semi-analytical dispersion relation based on lowest-order solutions to the gyrokinetic equations…
Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term…
We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…