Related papers: A Minimalist Approach to Rolling Wheels
The problem considered first by I. Newton (1687) consists in finding a surface of the minimal frontal resistance in a parallel flow of non-interacting point particles. The standard formulation assumes that the surface is convex with a given…
In this paper, we derive several formulas of counting families of non-intersecting paths for two-sided ladder-shaped regions. As an application, we give a new proof to a combinatorial interpretation of Fibonacci numbers obtained by G.…
Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that…
The classical theory of regularity of embeddings of compact convex sets was developed in the 1970s, exclusively in the real case, and even there it does not appear to have been stated in its simplest form. We begin by revisiting this…
In 1945 Einstein concluded that [1]: 'The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality…
In 1989 H. Tverberg proposed a quite general conjecture in Discrete geometry, which could be considered as the common basis for many results in Combinatorial geometry and at the same time as a discrete analogue of the common transversal…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…
We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…
The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in…
We examine closely the motion of the south-pointing chariot on a surface by taking into account the fact that both wheels have to roll without slipping. We firstly develop a procedure of successive approximations. In the limit where the…
We consider a nonholonomic system describing a rolling of a dynamically non-symmetric sphere over a fixed sphere without slipping. The system generalizes the classical nonholonomic Chaplygin sphere problem and it is shown to be integrable…
Let $X$ be a random variable that takes its values in $\frac{1}{q}\mathbb{Z}$, for some integer $q\ge2$, and consider $X$ rounded to an integer, either downwards or upwards or to the nearest integer. We give general formulas for the…
With the help of a two-dimensional model we study rolling lubrication by circular (2D fullerenes) molecules for a wide range of parameters. The conditions under which microscopic rolling friction may be effective are identified and related…
We investigate rough differential equations with a time-dependent reflecting lower barrier, where both the driving (rough) path and the barrier itself may have jumps. Assuming the driving signals allow for Young integration, we provide…
We present a one dimensional model for the development of corrugations in roads subjected to compressive forces from a flux of cars. The cars are modeled as damped harmonic oscillators translating with constant horizontal velocity across…
In the early 2000's the first and second named authors worked for a period of six years in an attempt of proving the Compositional Shuffle Conjecture [1]. Their approach was based on the discovery that all the Combinatorial properties…
Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. Introducing an approximation,…
We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, such schemes cannot accurately represent…