Simulation study of overtaking of ion-acoustic solitons in the fully kinetic regime

The overtaking collisions of ion-acoustic solitons (IASs) in presence of trapping effects of electrons are studied based on a fully kinetic simulation approach. The method is able to provide all the kinetic details of the process alongside the fluid-level quantities self consistently. Solitons are produced naturally by utilizing the chain formation phenomenon, then are arranged in a new simulation box to test different scenarios of overtaking collisions. Three achievements are reported here. Firstly, simulations prove the long-time life span of the ion-acoustic solitons in the presence of trapping effect of electrons (kinetic effects), which serves as the benchmark of the simulation code. Secondly, their stability against overtaking mutual collisions is established by creating collisions between solitons with different number and shapes of trapped electrons, i.e. different trapping parameter. Finally, details of solitons during collisions for both ions and electrons are provided on both fluid and kinetic levels. These results show that on the kinetic level, trapped electron population accompanying each of the solitons are exchanged between the solitons during the collision. Furthermore, the behavior of electron holes accompanying solitons contradicts the theory about the electron holes interaction developed based on kinetic theory. They also show behaviors much different from other electron holes witnessed in processes such as nonlinear Landau damping (Bernstein-Greene-Kruskal -BGK- modes) or beam-plasma interaction (like two-beam instability).Comment: 9 pages, 11 figures, accepted for publication in Physics of Plasma

Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.Comment: 12 pages, 6 figure

On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Simplified models for photohadronic interactions in cosmic accelerators

We discuss simplified models for photo-meson production in cosmic accelerators, such as Active Galactic Nuclei and Gamma-Ray Bursts. Our self-consistent models are directly based on the underlying physics used in the SOPHIA software, and can be easily adapted if new data are included. They allow for the efficient computation of neutrino and photon spectra (from pi^0 decays), as a major requirement of modern time-dependent simulations of the astrophysical sources and parameter studies. In addition, the secondaries (pions and muons) are explicitely generated, a necessity if cooling processes are to be included. For the neutrino production, we include the helicity dependence of the muon decays which in fact leads to larger corrections than the details of the interaction model. The separate computation of the pi^0, pi^+, and pi^- fluxes allows, for instance, for flavor ratio predictions of the neutrinos at the source, which are a requirement of many tests of neutrino properties using astrophysical sources. We confirm that for charged pion generation, the often used production by the Delta(1232)-resonance is typically not the dominant process in Active Galactic Nuclei and Gamma-Ray Bursts, and we show, for arbitrary input spectra, that the number of neutrinos are underestimated by at least a factor of two if they are obtained from the neutral to charged pion ratio. We compare our results for several levels of simplification using isotropic synchrotron and thermal spectra, and we demonstrate that they are sufficiently close to the SOPHIA software.Comment: Treatment of high energy interactions refined, additional black body benchmark added (v2), some references corrected (v3). A Mathematica notebook which illustrates the implementation of one model can be found at http://theorie.physik.uni-wuerzburg.de/~winter/Resources/AstroModel/Sim-B.html . 46 pages, 14 (color) figures, 7 tables. Final version, accepted for publication in Ap

Particle scattering in turbulent plasmas with amplified wave modes

High-energy particles stream during coronal mass ejections or flares through the plasma of the solar wind. This causes instabilities, which lead to wave growth at specific resonant wave numbers, especially within shock regions. These amplified wave modes influence the turbulent scattering process significantly. In this paper, results of particle transport and scattering in turbulent plasmas with excited wave modes are presented. The method used is a hybrid simulation code, which treats the heliospheric turbulence by an incompressible magnetohydrodynamic approach separately from a kinetic particle description. Furthermore, a semi-analytical model using quasilinear theory (QLT) is compared to the numerical results. This paper aims at a more fundamental understanding and interpretation of the pitch-angle scattering coefficients. Our calculations show a good agreement of particle simulations and the QLT for broad-band turbulent spectra; for higher turbulence levels and particle beam driven plasmas, the QLT approximation gets worse. Especially the resonance gap at μ = 0 poses a well-known problem for QLT for steep turbulence spectra, whereas test-particle computations show no problems for the particles to scatter across this region. The reason is that the sharp resonant wave-particle interactions in QLT are an oversimplification of the broader resonances in test-particle calculations, which result from nonlinear effects not included in the QLT. We emphasise the importance of these results for both numerical simulations and analytical particle transport approaches, especially the validity of the QLT. Appendices A-D are available in electronic form at http://www.aanda.or

Residence time and collision statistics for exponential flights: the rod problem revisited

Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.Comment: 9 pages, 8 figure

Direct instantons, topological charge screening and QCD glueball sum rules

Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on realistic instanton size distributions and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the 0^{-+} glueball signal) are traced to their neglect. On the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological short-distance physics strongly affects the sum rule results and reveals a rather diverse pattern of glueball properties. New predictions for the spin-0 glueball masses and decay constants and an estimate of the scalar glueball width are given, and several implications for glueball structure and experimental glueball searches are discussed.Comment: 49 pages, 8 figure

Normal Mode Determination of Perovskite Crystal Structures with Octahedral Rotations: Theory and Applications

Nuclear site analysis methods are used to enumerate the normal modes of $ABX_{3}$ perovskite polymorphs with octahedral rotations. We provide the modes of the fourteen subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns, which are obtained from rotations of the $BX_{6}$ octahedra with different sense and amplitude about high symmetry axes. We tabulate all normal modes of each tilt system and specify the contribution of each atomic species to the mode displacement pattern, elucidating the physical meaning of the symmetry unique modes. We have systematically generated 705 schematic atomic displacement patterns for the normal modes of all 15 (14 rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative examples how to use these tables to identify the octahedral rotations, symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing distortions of the $BX_{6}$ octahedra, and the associated Raman selection rules. We anticipate that these tables and schematics will be useful in understanding the lattice dynamics of bulk perovskites and would serve as reference point in elucidating the atomic origin of a wide range of physical properties in synthetic perovskite thin films and superlattices.Comment: 17 pages, 3 figures, 17 tables. Supporting information accessed through link specified within manuscrip