Related papers: Modelling circumplanetary ejecta clouds at low alt…
We investigate the evolution of the afterglow produced by the deceleration of the non-relativistic material due to its surroundings. The ejecta mass is launched into the circumstellar medium with equivalent kinetic energy expressed as a…
Humans will launch spacecraft that travel at an appreciable fraction of the speed of light. Spacecraft traffic will be tracked by radar. Scattering of pulsed electromagnetic fields by an object in uniform translational motion at…
Over the last decade, precise exoplanet transmission spectroscopy has revealed the atmospheres of dozens of exoplanets, driven largely by observatories like the Hubble Space Telescope. One major discovery has been the ubiquity of…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Numerous small bodies inevitably lead to cratering impacts on large planetary bodies during planet formation and evolution. As a consequence of these small impacts, a fraction of the target material escapes from the gravity of the large…
A projectile impact onto a granular target produces an ejecta curtain with the heterogeneous material distribution. Understanding how the heterogeneous pattern forms is potentially important for understanding how crater rays form. Previous…
The material that is ejected in a common-envelope (CE) phase in a close binary system provides an ideal environment for dust formation. By constructing a simple toy model to describe the evolution of the density and the temperature of CE…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
Earth-sized planets were observed in close-in orbits around M dwarfs. While more and more planets are expected to be uncovered around M dwarfs, theories of their formation and dynamical evolution are still in their infancy. We investigate…
We study the phenomena associated with the low-velocity impact of two solid discs of equal size using a cell model of brittle solids. The fragment ejection exhibits a jet-like structure the direction of which depends on the impact…
We derive a diffusion equation for light scattering from ejecta produced by extreme shocks on metallic samples. This model is easier to handle than a more conventional model based on the Radiative Transfer Equation (RTE), and is a relevant…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
Surface growth in random media is usually governed by both the surface tension and the random local forces. Simulations on lattices mimic the former by imposing a maximum gradient $m$ on the surface heights, and the latter by site-dependent…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
A stochastic model for a superposition of uncorrelated pulses with a random distribution of amplitudes, sizes, and velocities is analyzed. The pulses are assumed to move radially with fixed shape and amplitudes decreasing exponentially in…
The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a…
We study the influence of the matter content of extragalactic jets on their morphology, dynamics and emission properties. For this purpose we consider jets of extremely different compositions including pure leptonic and baryonic plasmas.…
Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between…