Related papers: The optimal angle of Release in Shot Put
It has been noted that in many professional sports leagues a good predictor of a team's won-loss percentage is Bill James' Pythagorean Formula RSobs^c / (RSobs^c + RAobs^c), where RSobs (resp. RAobs) is the observed average number of runs…
Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and…
A casino offers the following game. There are three cups each containing a die. You are being told that the dice in the cups are all the same, but possibly nonstandard. For a bet of \$1, the game master shakes all three cups and lets you…
The Five-hundred-metre Aperture Spherical Telescope (FAST) uses adaptive spherical panels to achieve a huge collecting area for radio waves. In this paper, we try to explore the optimal parameters for the curvature radius of spherical…
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The action of the wind is also taken into account, which…
Forecasting sporting events encapsulate a compelling intellectual endeavor, underscored by the substantial financial activity of an estimated $80 billion wagered in global sports betting during 2022, a trend that grows yearly. Motivated by…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule…
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a well investigated phase field model including contact line…
The prevailing models for advancing dynamic contact angle are under intensive debates, and the fitting performances are far from satisfying in practice. The present study proposes a model based on the recent understanding of the multi-scale…
Many have dedicated their time trying to determine the ideal conditions for a cylinder to have equal probabilities of falling with one of its faces facing upwards or on its side. However, to this day, there is no concrete analysis of what…
Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its…
We consider the blow-up sets and the upper blow-up rate estimates for two parabolic problems defined in a ball.
Performance measures such as stride length in athletics and the pace of runners can be estimated using different tricks such as measuring the number of steps divided by the running length or helping with markers printed on the track.…
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…
We present a new way of estimation of the role of chance in achieving success, by comparing the empirical data from 100-meter dash competitions (one of the sports disciplines with the most stringent controls of external randomness), with…
The introduction of optical tracking data across sports has given rise to the ability to dissect athletic performance at a level unfathomable a decade ago. One specific area that has seen substantial benefit is sports science, as high…
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. However, automating them, e.g., for high-throughput applications, does rarely involve…