Related papers: Investigating the classical problem of pursuit, in…
We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. The problem is…
The motion of celestial bodies in astronomy is closely related to the orbits of electrons encircling an atomic nucleus. Bohr and Sommerfeld presented a quantization scheme of the classical orbits to analyze the eigenstates of the hydrogen…
In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem…
Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the…
Pursuit-evasion is a multi-agent sequential decision problem wherein a group of agents known as pursuers coordinate their traversal of a spatial domain to locate an agent trying to evade them. Pursuit evasion problems arise in a number of…
A theory of self-propelled particles is developed in two dimensions assuming that the particles can be deformed from a circular shape when the propagating velocity is increased. A coupled set of equations in terms of the velocity and a…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
We study the motion of $N$ particles moving on a two-dimensional triangular lattice, whose sites are occupied by either left or right rotators. These rotators deterministically scatter the particles to the left (right), changing orientation…
A review of discrete quantum walk with two particle is given. The use of different states encountered in identical particle, and the idea of entanglement and superposition is explored to explored the interesting dynamics of two particle…
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…
This paper investigates the motion of falling leaves through modeling using papers and the corresponding data collected from more than four thousands experiments. Two series of experiments were designed in order to study the relationship…
In this article the one-dimensional, overdamped motion of a classical particle is considered, which is coupled to a thermal bath and is drifting in a quenched disorder potential. The mobility of the particle is examined as a function of…
This report studies the emergent behavior of systems of agents performing cyclic pursuit controlled by an external broadcast signal detected by a random set of the agents. Two types of cyclic pursuit are analyzed: 1)linear cyclic pursuit,…
The concept of entanglement in systems where the particles are indistinguishable has been the subject of much recent interest and controversy. In this paper we study the notion of entanglement of particles introduced by Wiseman and Vaccaro…
We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric equivalence between repelling particles and attracting…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
Consider the dynamics of two point masses on a surface of constant curvature subject to an attractive force analogue of Newton's inverse square law. When the distance between the bodies is sufficiently small, the reduced equations of motion…