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In the field of bioimaging, an important part of analyzing the motion of objects is tracking. We propose a method that applies the Sinkhorn distance for solving the optimal transport problem to track objects. The advantage of this method is…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and…
Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic…
This paper considers the problem of finding a quickest path between two points in the Euclidean plane in the presence of a transportation network. A transportation network consists of a planar network where each road (edge) has an…
Scientists from the OPERA experiment have measured neutrinos supposedly travelling at a velocity faster than light contrary to the theory of relativity. Even when the measurements are precise, the interpretation of this problem is being…
Numerical simulation of high-speed turbulent water jets in air and its validation with experimental data has not been reported in the literature. It is therefore aimed to simulate the physics of these high-speed water jets and compare the…
Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or…
In the infinite regular tree $\mathbb{T}_{q+1}$ with $q \in \mathbb{Z}_{\ge 2}$, we consider families $\{\mu_u^n\}$, indexed by vertices $u$ and nonnegative integers ("discrete time steps") $n$, of probability measures such that $\mu_u^n(v)…
We investigate the occupancy statistics of birds on a wire and on higher-dimensional substrates. In one dimension, birds land one by one on a wire and rest where they land. Whenever a newly arriving bird lands within a fixed distance of…
In this paper, a solution to Zeno's paradox of motion was offered and a possible, based on observations and empirical viewpoint, interpretation. A gedanken experiment was proposed in accordance to our empirical and experimental paradigm,…
Experimental analysis of the motion in a system of two coupled oscillators with arbitrary initial conditions was performed and the normal coordinates were obtained directly. The system consisted of two gliders moving on an air track, joined…
In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model's output. We first show…
Understanding how sound propagates through different media is fundamental to both science and technology. While sound plays a critical role in natural navigation and underlies a wide range of applications - from medical ultrasound to sonar…
When a large collection of objects (e.g., robots, sensors, etc.) has to be deployed in a given environment, it is often required to plan a coordinated motion of the objects from their initial position to a final configuration enjoying some…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
For thermal transport in one-dimensional (1D) systems, recent studies have suggested that employing different theoretical models and different numerical simulations under different system's parameter regimes might lead to different…
Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a…