Related papers: How to run 100 meters ?
Consider a branching random walk evolving in a macroscopic time-inhomogeneous environment, that scales with the length $n$ of the process under study. We compute the first two terms of the asymptotic of the maximal displacement at time $n$.…
The biomechanics of the human body allow humans a range of possible ways of executing movements to attain specific goals. Nevertheless, humans exhibit significant patterns in how they execute movements. We propose that the observed patterns…
The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order…
We present a mathematical model for optimizing breakaway strategies in competitive cycling, balancing power expenditure, aerodynamic drag, and crashing. Our framework incorporates probabilistic crash dynamics, allowing a cyclist's risk…
In the racetrack acceleration model, proposed by Martin Gardner in 1973, each step consists of changing the position of the vehicle by a vector in $\mathbb{Z}^2$, with the constraints that two consecutive vectors differ by at most one unit…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
Predicting cycling duration for a given route is essential for training planning and event preparation. Existing solutions rely on physics-based models that require extensive parameterization, including aerodynamic drag coefficients and…
The levels of agility and flight or swimming performance demonstrated by insects, birds, fish, and even some aquatic invertebrates, are often vastly superior to what even the most advanced human-engineered vehicles operating in the same…
This paper studies bipedal locomotion as a nonlinear optimization problem based on continuous and discrete dynamics, by simultaneously optimizing the remaining step duration, the next step duration and the foot location to achieve…
We present a framework that gives a deep insight into the link between physical and technical-tactical aspects of soccer and it allows associating physical performance with value generation thanks to a top-down approach. First, we estimate…
We study the asymptotic behaviour of random walks in i.i.d. random environments on $\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when…
Many studies on one-on-one pursuit-evasion problems have shown that formulas about the pursuer's trajectory can be solved by supposing three conditions. First, the evader follows specific figures. Second, the pursuer's velocity vector…
Optimization of energy cost determines average values of spatio-temporal gait parameters such as step duration, step length or step speed. However, during walking, humans need to adapt these parameters at every step to respond to exogenous…
Efficient locomotion is important for the evolution of complex life, yet the physical principles selecting specific swimming strokes often remain entangled with biological constraints. In viscous fluids, the scallop theorem constrains the…
Micro- and nano-scale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally…
In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots…
Amateur marathon runners who exercise excessively over time have pathological structural changes in their hearts and aortas. Amateur marathon runners' cardiovascular system adaptations and dangers are discussed in this article. After…
The Lonely Runner Conjecture of Wills and Cusick states that if $k+1$ runners start running at distinct constant speeds around a unit-length circular track, then for each runner there is a time when he/she is at least $1/(k+1)$ away from…
Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or…
We analyze the time series of soccer matches in a model-free way using data for the German soccer league (Bundesliga). We argue that the goal difference is a better measure for the overall fitness of a team than the number of points. It is…