1,673 research outputs found

    Symmetric resonance based integrators and forest formulae

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    We introduce a unified framework of symmetric resonance based schemes which preserve central symmetries of the underlying PDE. We extend the resonance decorated trees approach introduced in arXiv:2005.01649 to a richer framework by exploring novel ways of iterating Duhamel's formula, capturing the dominant parts while interpolating the lower parts of the resonances in a symmetric manner. This gives a general class of new numerical schemes with more degrees of freedom than the original scheme from arXiv:2005.01649. To encapsulate the central structures we develop new forest formulae that contain the previous class of schemes and derive conditions on their coefficients in order to obtain symmetric schemes. These forest formulae echo the one used in Quantum Field Theory for renormalising Feynman diagrams and the one used for the renormalisation of singular SPDEs via the theory of Regularity Structures. These new algebraic tools not only provide a nice parametrisation of the previous resonance based integrators but also allow us to find new symmetric schemes with remarkable structure preservation properties even at very low regularity.Comment: 71 page

    Linear stability and numerical analysis of dipolar vortices and topographic flows

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    The linear stability and numerical analysis of geophysical flow patterns is carried out on the beta-plane in a quasigeostrophic approximation. We consider initial steady state dipoles in a one-and-a-half-layer model that are capable of zonal drift in either direction. Despite previous numerical works suggesting that eastward propagating dipoles are stable, our high resolution simulations identify the spontaneous symmetry breaking of weak dipoles over time. The evolution is associated with a growing critical mode with even symmetry about the zonal axis. On carrying out a linear stability analysis, the critical modes obtained share consistency with the numerical fields. In addition, both methods of analysis show that the linear growth rate is inversely proportional to the dipole intensity. Furthermore, the partner separation becomes more pronounced after the linear growth stage, suggesting that nonlinear effects play a pivotal role in the underlying dynamics. Beyond this, the dynamics of initially tilted dipoles and dipole-rider solutions are considered, while stronger dipoles are further analysed using the method of distillation. Flows over sinusoidal bottom relief are considered in a two-layer model on the quasigeostrophic beta-plane. Fourier mode solutions are assumed for the layer-wise perturbation field in order to carry out a linear stability analysis, from which a coupled eigenproblem is derived between fluid columns for both zonal and meridional bottom irregularities. The presence of zonally oriented multiple ridges stabilises an otherwise unstable homogeneous zonal current with respect to increases in the number of ridges and ridge amplitude. Moreover, a bifurcation occurs in the unstable mode spectra and is dependent on the number of ridges. The critical eigenmodes in this case are found to be eddy chains of alternating sign, and these share remarkable resemblance with those obtained numerically. Meridionally oriented multiple ridges are also considered, but are found not to affect the maximum growth rate directly.Open Acces

    Transient fields of coherent synchrotron radiation in a rectangular pipe

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    We found an exact analytical solution of the wave equation for a transient electromagnetic field of synchrotron radiation in the frequency domain. The exact solution represents the field which consists of the coherent and incoherent components of synchrotron radiation and the space charge field of the particle beam moving in a bending magnet. The field in the time domain is gotten by numerically Fourier transforming the values of the field calculated using the exact solution. The beam has an arbitrary charge density and current density which satisfy the equation of continuity. The beam is moving in a perfectly conducting rectangular pipe which is uniformly curved in a semi-infinite bending magnet. The exact solution is not self-consistent, i.e., this is an exact expression of the field for a given beam current. We do not solve the equation of motion of the beam in the present paper. On the basis of the exact expression of the field found in the present study, we discuss the applicability and accuracy of the paraxial approximation which is sometimes used to calculate the field and spectrum of coherent or incoherent synchrotron radiation

    Electron Thermal Runaway in Atmospheric Electrified Gases: a microscopic approach

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    Thesis elaborated from 2018 to 2023 at the Instituto de Astrofísica de Andalucía under the supervision of Alejandro Luque (Granada, Spain) and Nikolai Lehtinen (Bergen, Norway). This thesis presents a new database of atmospheric electron-molecule collision cross sections which was published separately under the DOI : With this new database and a new super-electron management algorithm which significantly enhances high-energy electron statistics at previously unresolved ratios, the thesis explores general facets of the electron thermal runaway process relevant to atmospheric discharges under various conditions of the temperature and gas composition as can be encountered in the wake and formation of discharge channels

    3D RMHD simulations of jet-wind interactions in high-mass X-ray binaries

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    Context. Relativistic jets are ubiquitous in the Universe. In microquasars, especially in high-mass X-ray binaries, the interaction of jets with the strong winds driven by the massive and hot companion star in the vicinity of the compact object is fundamental for understanding the jet dynamics, nonthermal emission, and long-term stability. However, the role of the jet magnetic field in this process is unclear. In particular, it is still debated whether the magnetic field favors jet collimation or triggers more instabilities that can jeopardize the jet evolution outside the binary. Aims. We study the dynamical role of weak and moderate to strong toroidal magnetic fields during the first several hundred seconds of jet propagation through the stellar wind, focusing on the magnetized flow dynamics and the mechanisms of energy conversion. Methods. We developed the code Lóstrego v1.0, a new 3D relativistic magnetohydrodynamics code to simulate astrophysical plasmas in Cartesian coordinates. Using this tool, we performed the first 3D relativistic magnetohydrodynamics numerical simulations of relativistic magnetized jets propagating through the clumpy stellar wind in a high-mass X-ray binary. To highlight the effect of the magnetic field in the jet dynamics, we compared the results of our analysis with those of previous hydrodynamical simulations. Results. The overall morphology and dynamics of weakly magnetized jet models is similar to previous hydrodynamical simulations, where the jet head generates a strong shock in the ambient medium and the initial overpressure with respect to the stellar wind drives one or more recollimation shocks. On the timescales of our simulations (i.e., t < 200 s), these jets are ballistic and seem to be more stable against internal instabilities than jets with the same power in the absence of fields. However, moderate to strong toroidal magnetic fields favor the development of current-driven instabilities and the disruption of the jet within the binary. A detailed analysis of the energy distribution in the relativistic outflow and the ambient medium reveals that magnetic and internal energies can both contribute to the effective acceleration of the jet. Moreover, we verified that the jet feedback into the ambient medium is highly dependent on the jet energy distribution at injection, where hotter, more diluted and/or more magnetized jets are more efficient. This was anticipated by feedback studies in the case of jets in active galaxies

    Drift-diffusion models for innovative semiconductor devices and their numerical solution

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    We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization

    Fast heating by feedback flow control

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