Related papers: Throwing and jumping for maximum horizontal range
An adjoint-based optimization is applied to study the thrust performance of a pitching-rolling ellipsoidal plate in a uniform stream at Reynolds number 100. To achieve the highest thrust, the optimal kinematics of pitching-rolling motion is…
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…
We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the…
It is common to relate the dynamic contact angle $\theta_d$ to the relative speed between the substrate and the contact line; theory suggests $\theta_d^3 \propto U$. In fact, available physical models show that the dynamic angle involves…
This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper…
The tree-based rope swing is a popular recreation facility, often installed in outdoor areas, giving pleasure to thrill-seekers. In the setting, one drops down from a high platform, hanging from a rope, then swings at a great speed like…
We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is a remote sensor (e.g., a radar station) that can sense the evader's location upon a…
Among probability measures on $d$-dimensional real projective space, one which maximizes the expected angle $\arccos(\frac{x}{|x|}\cdot \frac{y}{|y|})$ between independently drawn projective points $x$ and $y$ was conjectured to…
We employ the novel theory of heterogeneous extreme value statistics to accurately estimate the ultimate world records for the 100-m running race, for men and for women. For this aim we collected data from 1991 through 2023 from thousands…
Spin plays a pivotal role in ball-based sports. Estimating spin becomes a key skill due to its impact on the ball's trajectory and bouncing behavior. Spin cannot be observed directly, making it inherently challenging to estimate. In table…
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…
A quick and fun investigation into the effects of correcting for wind assistance/resistance and drag on 100m sprint performances. Considered are World 100m rankings, as well as Canadian rankings
We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…
In drone racing, the time-minimum trajectory is affected by the drone's capabilities, the layout of the race track, and the configurations of the gates (e.g., their shapes and sizes). However, previous studies neglect the configuration of…
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean…
The use of drones or Unmanned Aerial Vehicles (UAVs) for aerial photography and cinematography is becoming widespread. The following optimization problem has been recently considered. Let us imagine a sporting event where a group of runners…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
The numerical prediction of droplet base radius and contact angle depends on the choice of characteristic radius and height of droplet. In this study, a developed model on the basis of lubrication approximation is used to investigate the…
The block maximum method, which is widely used in extreme value analysis, uses a generalized extreme value distribution to approximate that of the maximum of m observations. The quality of this approximation depends on the value of m and…
This paper deals with a projection least squares estimator of the drift function of a jump diffusion process $X$ computed from multiple independent copies of $X$ observed on $[0,T]$. Risk bounds are established on this estimator and on an…