Related papers: Investigating the classical problem of pursuit, in…
We describe and analyze a generalization of the classic ``Four Bugs on a Square'' cyclic pursuit problem. Instead of allowing the bugs to spiral towards one another, we constrain $N$ bugs to the perimeter of the unit circle. Depending on…
In this article, I discuss the motion of $N$ point masses in non-relativistic mechanics, when the interaction between them is purely the Newtonian gravitational interaction, with $N$ greater than or equal to 2. The dynamical equations of…
Multiple Object Tracking (MOT) has gained increasing attention due to its academic and commercial potential. Although different approaches have been proposed to tackle this problem, it still remains challenging due to factors like abrupt…
We extend the traditional problem of calculating the traveled distance of a fly that is moving with constant speed on a straight path between two trains that are approaching one another, we found two analytical solutions for the traditional…
Projection pursuit is used to find interesting low-dimensional projections of high-dimensional data by optimizing an index over all possible projections. Most indexes have been developed to detect departure from known distributions, such as…
We discuss the collective dynamics of self-propelled particles with selective attraction and repulsion interactions. Each particle, or individual, may respond differently to its neighbors depending on the sign of their relative velocity.…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
We consider a moving target and an active pursing agent, modeled as an intelligent active Brownian particle capable of sensing the instantaneous target location and adjust its direction of motion accordingly. An analytical and simulation…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we…
We study a system of self-propelled particles which interact with their neighbors via alignment and repulsion. The particle velocities result from self-propulsion and repulsion by close neighbors. The direction of self-propulsion is…
We consider a mathematical model for a two-particle system driven by the spatial gradient of a concentration field of chemicals with conservative attractive interactions in one dimension. This setup corresponds to an experimental system…
Given a two-dimensional polygonal space, the multi-robot visibility-based pursuit-evasion problem tasks several pursuer robots with the goal of establishing visibility with an arbitrarily fast evader. The best known complete algorithm for…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
We investigate the relativistic generalization of the classical St\"{o}rmer problem, which describes the motion of charged particles in a purely magnetic dipole field. By incorporating special relativistic effects, the particle dynamics is…
Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate…
This paper studies the problem of detection and tracking of general objects with long-term dynamics, observed by a mobile robot moving in a large environment. A key problem is that due to the environment scale, it can only observe a subset…