Related papers: Estimation of $\pi$ via experiment

We discuss a method for calculating $ \pi $ using elastic collision between two masses $ M $ and $ m $, with $ X = m/M = 10^{2(1-d)} $ where $ d $ is an integer, and a wall. The total number of collisions between $ M $, $ m $ and the wall…

There are two popular ways to speed up simulations of planet formation via increasing the collision probability: ({\it i}) confine motion to 2D, ({\it ii}) artificially enhance the physical radii of the bodies by an expansion factor. In…

A method of obtaining the number pi is considered, which derives pi from the number of elastic collisions between two blocks and a wall.

This paper presents a novel approach to numerically describe the interactions between rigid bodies, with a special focus on robotic grasping. Some of the more common approaches used to address such issues rely on satisfaction of a set of…

We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly),…

An investigation of the comparative efficiency of the different methods in which {\pi} is cal- culated. This thesis will compare and contrast five different methods in calculating {\pi} by first deriving the various proofs to each method…

The {\pi}-{\pi} interactions between organic molecules are among the most important parameters for optimizing the transport and optical properties of organic transistors, light-emitting diodes, and (bio-) molecular devices. Despite…

A method is developed to calculate collision probability in this paper. Based on the encounter geometric features of space objects, it is reasonable to separate the radial orbital motions from that in the cross section for most encounter…

We propose to use the coincidence method of Ma to measure an entropy of the system created in heavy ion collisions. Moreover we estimate, in a simple model, the values of parameters for which the thermodynamical behaviour sets in.

We revisit the computation of a probability of collision in the context of automotive collision avoidance (also referred to as conflict detection in other contexts). After reviewing existing approaches to the definition and computation of a…

We develop a formalism for calculating probabilities for the outcomes of stellar dynamical interactions, based on results from $N$-body scattering experiments. We focus here on encounters involving up to six particles and calculate…

For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…

Predicting a potential collision with leading vehicles is an essential functionality of any autonomous/assisted driving system. One bottleneck of existing vision-based solutions is that their updating rate is limited to the frame rate of…

In a Keplerian system, a large number of bodies orbit a central mass. Accretion disks, protoplanetary disks, asteroid belts, and planetary rings are examples. Simulations of these systems require algorithms that are computationally…

Direct collisions between finite-sized particles occur commonly in many areas of astrophysics. Such collisions are typically mediated by chaotic, bound gravitational interactions involving small numbers of particles. An important…

We investigate the outcome of collisions in very different mass regimes, but an otherwise identical parameter setup, comprising the impact velocity ($v/v_\mathrm{esc}$), impact angle, mass ratio, and initial composition, w.r.t. simple…

In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance…

A novel algorithm is presented for the estimation of collision probabilities between dynamic objects with uncertain trajectories, where the trajectories are given as a sequence of poses with Gaussian distributions. We propose an adaptive…

We use a simple, collision-based, discrete, random abrasion model to compute the profiles for the stoss faces in a bedrock abrasion process. The model is the discrete equivalent of the generalized version of a classical, collision based…

Real-time safety systems are crucial components of intelligent vehicles. This paper introduces a prediction-based collision risk assessment approach on highways. Given a point mass vehicle dynamics system, a stochastic forward reachable set…