Related papers: Brachistochrone on a Velodrome
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…
The travel time tomography problem is a coefficient inverse problem for the eikonal equation. This problem has well known applications in seismic. The eikonal equation is considered here in the circular cylinder, where point sources run…
Clustering trajectories is a central challenge when faced with large amounts of movement data such as GPS data. We study a clustering problem that can be stated as a geometric set cover problem: Given a polygonal curve of complexity $n$,…
An airplane flying at constant speed and altitude is an example of physics invisible to the pilots and passengers, but visible to remote observers and manifest in the mathematics. The optimum flight path is an arc of a Great Circle,…
Automated chemical synthesis, materials fabrication, and spectroscopic physical measurements often bring forth the challenge of process trajectory optimization, i.e., discovering the time dependence of temperature, electric field, or…
This paper introduces the \emph{$d$-distance $b$-matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges, an integer $d\in\mathbb{Z}_+$ and a degree bound function…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
Circular orbits of a particle sliding on a frictionless surface of revolution about a vertical axis are unstable below a critical radius if the curvature of the surface satisfies a specified condition. This behavior can be realized in a…
This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called…
Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…
We introduce a `virtual-move' Monte Carlo (VMMC) algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an…
The motion of pedestrians is subject to a wide range of influences and exhibits a rich phenomenology. To enable precise measurement of the density and velocity we use an alternative definition using Voronoi diagrams which exhibits smaller…
The problem of simultaneous trajectography of several dynamical objects is formulated as an optimization problem. The available observations consist in a series of photographs showing undiscriminated objects. The goal is to find the object…
We develop a new method to determine the acceleration of a block sliding down along the face of a moving wedge. We have been able to link the solution of this problem to that of the inclined plane problem of elementary physics, thus…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Light has a fascinating property: it always travels the path that takes the least time between any two points. This is the motivating property behind optical phenomena such as Reflection and Refraction. The unreasonable economic efficiency…
This paper investigates optimal takeoff trajectory planning for a quadrotor modeled with vertical-plane rigid body dynamics in an uncertain, one-dimensional wind-field. The wind-field varies horizontally and propagates across an operating…
The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…
Lambert's problem is a classical boundary value problem in analytical mechanics. It arises when trying to determine the energy required to place a particle, subject to a central gravitational potential, in a "free fall" trajectory…
This study addresses optimal impulsive trajectory design within the Circular Restricted Three-Body Problem (CR3BP), presenting a global optimization-based approach to identify minimum $\Delta V$ transfers between periodic orbits, including…