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Particles moving inside a fluid near, and interacting with, invariant manifolds is a common phenomenon in a wide variety of applications. One elementary question is whether we can determine once a particle has entered a neighbourhood of an…
This work is basically about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics.…
The "twin paradox" of special relativity offers the possibility to make interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
In this paper, we make an important step towards the black-box machine teaching by considering the cross-space machine teaching, where the teacher and the learner use different feature representations and the teacher can not fully observe…
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the…
In this paper, we consider a mobility system of travelers and providers, and propose a "mobility game" to study when a traveler is matched to a provider. Each traveler seeks to travel using the services of only one provider, who manages one…
We introduce an extension of the fellow traveler property which allows fellow travelers to be at distance bounded from above by a function $f(n)$ growing slower than any linear function. We study normal forms satisfying this extended fellow…
Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
Consider a stationary agent A at an unknown location and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own…
This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…
Flying Gyroscopes are fascinating flight objects, which, due to gyroscopic stabilization, can achieve surprisingly long flight distances when thrown with rapid spin. The most common example hereby is a traditional Frisbee disc. This paper…
A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global…
An analysis of traveling wave solutions of pure cross-diffusion systems, i.e., systems that lack reaction and self-diffusion terms, is presented. Using the qualitative theory of phase plane analysis the conditions for existence of different…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the…
The motion of particles hit by a burst of gravitational waves generated by flyby admits, for the derivative-of-the-Gaussian profile, only a numerical description. The profile can however be approximated by the hyperbolic Scarf potential…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
Biological and artificial neural systems form high-dimensional neural representations that underpin their computational capabilities. Methods for quantifying geometric similarity in neural representations have become a popular tool for…