Related papers: Cycloid Experiment for freshmen physics labs
We prove that a bounded domain $\Omega$ in $\R^n$ with smooth boundary has a periodic billiard trajectory with at most $n+1$ bounce times and of length less than $C_n r(\Omega)$, where $C_n$ is a positive constant which depends only on $n$,…
Using the theory of optimal rocket trajectories in general relativity, recently developed in arXiv:1105.5235, we present a candidate for the minimum total integrated acceleration closed timelike curve in the Godel universe, and give…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
The spin foam framework provides a way to define the dynamics of canonical loop quantum gravity in a spacetime covariant way, by using a path integral over histories of quantum states which can be interpreted as `quantum space-times'. This…
It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon…
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical…
We investigated how students apply the concept of circulation when faced with problems related to the Ampere-Maxwell law. For this purpose, we designed a metacognitive pencil-and-paper question, presented it to 65 students, and analysed…
This manuscript discusses gravity tunnels formed by connecting two vertical shafts by a constant-radius tunnel within the Earth, which featured in a dream I had in September 2024. The total travel time through such a tunnel can be minimized…
In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year…
We describe a simple mechanical system that operates as a ponderomotive particle trap, consisting of a circular hoop and a frictionless bead, with the hoop rotating about a horizontal axis lying in the plane of the hoop. The bead in the…
We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…
The aim of these lectures is to give an introduction to several topics which lie at the intersection of string theory, gravity theory and gravity phenomenology. One successively reviews: (i) the "membrane" approach to the dissipative…
H${\acute{e}}$non [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point…
Quantum billiards have been simulated so far in many ways, but in this work a new aproximation is considerated. This study is based on the quantum billiard already obtained by others authors via a tensor product of two 1-D quantum walks .…
Consider the random subgraph process on a base graph $G$ with $n$ vertices: we generate a sequence $\{G_t\}_{t=0}^{|E(G)|}$ by taking a uniformly random ordering of the edges of $G$ and then adding these edges one by one to the empty graph…
We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three…
We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only…
The paper gives a review of very recent results related to the Poncelet Theorem, on the occasion of its bicentennial. We are telling the story of one of the most beautiful theorems of Geometry, recalling for the general mathematical…
The present work analyses the particle motion in the Van Stockum space-time considering the existence of closed timelike curves. Test particles with or without angular momentum are studied in the present geometry. It is found that only…