Related papers: Order statistics and heavy-tail distributions for …
The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations…
We present Monte Carlo simulations of the dynamical evolution of the Oort cloud over the age of the Solar System, using an initial sample of one million test comets without any cloning. Our model includes perturbations due to the Galactic…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
Comets in the Oort cloud evolve under the influence of internal and external perturbations, such as giant planets, stellar passages, and the galactic tidal field. We aim to study the dynamical evolution of the comets in the Oort cloud,…
This paper explores the stability of an Earth-like planet orbiting a solar-mass star in the presence of a stellar companion using ~ 400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a…
The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or…
Our understanding of the mechanisms governing the structure and secular evolution galaxies assume nearly integrable Hamiltonians with regular orbits; our perturbation theories are founded on the averaging theorem for isolated resonances. On…
We study the evolution of long-period comets by numerical integration of their orbits, following comets from their origin in the Oort cloud until their final escape or destruction, in a model solar system consisting of the Sun, the four…
The formation of large-scale vortices is an intriguing phenomenon in two-dimensional turbulence. Such organization is observed in large-scale oceanic or atmospheric flows, and can be reproduced in laboratory experiments and numerical…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…
We show that the effects of radial galactic tides alone can change the dynamics of an Oort cloud of comets around a star in a highly sensitive manner. The Oort cloud dynamics depends primarily from the star's position in the Galaxy and its…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
Statistical properties of circulation encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, as the dependence of circulation…
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…
Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions…
MHD Turbulence is a critical component of the current paradigms of star formation, particle transport, magnetic reconnection and evolution of the ISM. Progress on this difficult subject is made via numerical simulations and observational…
The tangled nodal lines (wave vortices) in random, three-dimensional wavefields are studied as an exemplar of a fractal loop soup. Their statistics are a three-dimensional counterpart to the characteristic random behaviour of nodal domains…