Related papers: Maximum range of a projectile thrown from constant…

In any spatially discrete model of pedestrian motion which uses a regular lattice as basis, there is the question of how the symmetry between the different directions of motion can be restored as far as possible but with limited…

Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…

We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot…

We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown $d$-dimensional $\mathcal{C}^k$-smooth submanifold of $\mathbb{R}^D$, we…

Safe and smooth motion control is essential for mobile robots when performing various automation tasks around obstacles, especially in the presence of people and other mobile robots. The total turning and space used by a mobile robot while…

As a first step in the project of ratchet optimisation, the optimal driving waveform among a wide class of admissible functions for an overdamped, adiabatic rocking ratchet is shown to be dichotomous. `Optimum' is defined as that which…

Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…

We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The…

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…

The general properties needed in targets (sources) for high precision, high accuracy measurements are reviewed. The application of these principles to the problem of developing targets for the Fission TPC is described. Longer term issues,…

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a…

The energy characteristics of a relativistic charged particle in the field of a plane electromagnetic wave of a given amplitude are studied. The dependence of the particle's energy on its phase coordinate is obtained. The maximum value of…

A general method is presented for determining the maximum electric energy in a bounded region of optical fields with given time-averaged flux of electromagnetic energy. Time-harmonic fields are considered whose plane wave expansion consists…

We carry out experiments of 104 m/s velocity oblique impacts into a granular medium (sand). Impact craters have nearly round rims even at a grazing angle of about $10^\circ$, however, the strength of seismic pulses excited by the impact is…

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…

This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…

The maximum surveillance of a target which is holding course is considered, wherein an observer vehicle aims to maximize the time that a faster target remains within a fixed-range of the observer. This entails two coupled phases: an…

Due to the importance of collisions and impacts in early phases of the evolution of the planetary system, it is interesting to estimate the heating of a solid target due to an impact in it . A physically simple calculation of the…

This contribution is a first step aiming to address a general question: what can be concluded on impact craters which exist on various planetary system objects, by combining astronomical data and known theoretical results from solid state…

Deployment of robotic systems in the real world requires a certain level of robustness in order to deal with uncertainty factors, such as mismatches in the dynamics model, noise in sensor readings, and communication delays. Some approaches…