Related papers: The bullet problem with discrete speeds
We introduce a novel 'one-shot' solution technique resolving an open problem (Karatzas et al., Finite-fuel singular control with discretionary stopping, Stochastics 71:1-2 (2000)). Unexpectedly given the convexity of the latter problem, its…
The Standard Model of particle physics predicts the speed of light to be a universal speed of propagation of massless carriers. However, other possibilities exist -- including Lorentz-violating theories -- where different fundamental fields…
This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called…
The invariance of the speed of light implies a series of consequences related to our perception of simultaneity and of time itself. Whilst these consequences are experimentally well studied for subluminal speeds, the kinematics of…
Self-stabilization ensures that, after any transient fault, the system recovers in a finite time and eventually exhibits a correct behaviour. Speculation consists in guaranteeing that the system satisfies its requirements for any execution…
Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…
The TASEP (totally asymmetric simple exclusion process) is a basic model for an one-dimensional interacting particle system with non-reversible dynamics. Despite the simplicity of the model it shows a very rich and interesting behaviour. In…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
The unique properties of dark matter are revealed during collisions between clusters of galaxies, like the bullet cluster (1E 0657-56) and baby bullet (MACSJ0025-12). These systems provide evidence for an additional, invisible mass in the…
We study the asymptotic speed of a second class particle in the two-species asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$ with each particle belonging either to the first class or the second class. For any fixed non-negative…
Consider the model where particles are initially distributed on $\mathbb{Z}^d, \, d\geq 2$, according to a Poisson point process of intensity $\lambda>0$, and are moving in continuous time as independent simple symmetric random walks. We…
We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy ``piston'', with elastic collisions between particles but inelastic collisions between the light particles and the interval…
An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
(Abridged) In this celebratory contribution, we present some new data from standard star cluster modelling containing primordial binaries and triples, as well as results from a binary black hole simulation with two massive members. In the…
We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at…
One considers the motion of a test particle in an homogeneous fluid in equilibrium at temperature $T$, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still posseses a…
We consider the trapping reaction A + B -> B in space dimension d<=2. By formally eliminating the B particles from the problem we derive an effective dynamics for the A particles from which the survival probability of a given A particle and…
Several differential equations usually appearing in mathematical physics are solved through a power series expansion, which reduces in solving difference equations. In this paper a probability problem is presented whose solution follows a…
We present accurate measurements of the relative motion and deformation of two large bubbles released consecutively in a quiescent liquid confined in a thin-gap cell. Though the second bubble injected is smaller, we observed that in all…