Related papers: Brachistochrone on a Velodrome
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
We consider the problem of computing the Fr\'echet distance between two curves for which the exact locations of the vertices are unknown. Each vertex may be placed in a given uncertainty region for that vertex, and the objective is to place…
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
Traffic-related pollution is becoming a major societal problem globally. Cyclists are particularly exposed to this form of pollution due to their proximity to vehicles' tailpipes. In a number of recent studies, it is been shown that…
The study of the motion of a rigid body on a plane (RBP motion) is usually one of the most challenging topics that students face in introductory physics courses. In this paper, we discuss a couple of problems which are typically used in…
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to…
The pursuit problem is a historical issue of the application of mathematics in physics, which has been discussed for centuries since the time of Leonardo Da Vinci, and its applications are wide ranging from military and industrial to…
To recover the long-time behavior and the statistics of molecular trajectories from the large number (tens of thousands) of their short fragments, obtained by super-resolution methods at the single molecule level, data analysis based on a…
The NP-hard Maximum Planar Subgraph problem asks for a planar subgraph $H$ of a given graph $G$ such that $H$ has maximum edge cardinality. For more than two decades, the only known non-trivial exact algorithm was based on integer linear…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
This paper provides (in french) a framework for an alternative demonstration of result of Khimshiashvili and Panina on the characterization of critical points of the area on the manifold of polygons with fixed sidelengths as being the…
Let $\s^1$ be a circle in Euclidean plane. We consider the problem of finding the shape of a planar curve which is an extremal of the potential energy that measures the distance to $\s^1$. We describe the shape of these curves…
The study of vortex flows in the vicinity of multiple solid obstacles is of considerable theoretical interest and practical importance. In particular, the case of flows past a circular cylinder placed above a plane wall has attracted a lot…
This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. The manuscript covers in a simple way…
We study the problem of finding neck-like features on a surface. Applications for such cuts include robotics, mesh segmentation, and algorithmic applications. We provide a new definition for a surface bottleneck -- informally, it is the…
Cyclic polytopes are characterized as simplicial polytopes satisfying Gale's evenness condition (a combinatorial condition on facets relative to a fixed ordering of the vertices). Periodically-cyclic polytopes are polytopes for which…
We study the problems of finding a minimum cycle basis (a minimum weight set of cycles that form a basis for the cycle space) and a minimum homology basis (a minimum weight set of cycles that generates the $1$-dimensional…
Given a set $S$ of $n$ static points and a free point $p$ in the Euclidean plane, we study a new variation of the minimum enclosing circle problem, in which a dynamic weight that equals to the reciprocal of the distance from the free point…
We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than…
The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test…