Related papers: A survival guide for feeble fish
We prove that the speed of a biased random walk on a supercritical Galton-Watson tree conditioned to survive is analytic within the ballistic regime. This extends the previous work arXiv:1906.07913 in which it was shown that the speed is…
Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation of waves along a body. As a mode of locomotion it is primitive and relatively simple, yet can be remarkably robust. No wonder then, that it is…
It is commonly assumed that fluid cannot slip along a solid surface. The experimental evidence generally supports this assumption. We demonstrate that when the change of the relative velocity of a fluid and a solid wall is sufficiently…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
Flagellated bacteria are hydrodynamically attracted to rigid walls, yet past work shows a 'hovering' state where they swim stably at a finite height above surfaces. We use numerics and theory to reveal the physical origin of hovering.…
Many different robots have been designed and built to work under water. In many cases, researchers have chosen to use bio-inspired platforms. In most cases, the main goal of the fish inspired robots has been set to autonomously swim and…
Empirical observations indicate striking similarities among locomotion in terrestrial animals, birds, and fish, but unifying physical grounds are lacking. When applied to efficient locomotion, the analytical mechanics principle of minimum…
During motion from deep to shallow water, multiple equilibria may emerge, each with identical drag - a phenomenon that can be explained by a localised amplification of the wave drag near the shallow wave speed. The implication of this is…
Understanding active electrolocation in weakly electric fish remains a challenging issue. In this article we propose a mathematical formulation of this problem, in terms of partial differential equations. This allows us to detail two…
The aim of this paper is to study the generalized Fisher-KPP equation with nonlocal diffusion. In specific we prove the existence of a critical speed so that traveling front type solutions exist up to this critical speed and non-existence…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
This paper examines the degree to which an evader seeking a safe and efficient path to a target location can benefit from increasing levels of knowledge regarding one or more range-limited pursuers seeking to intercept it. Unlike previous…
The considered model will be formulated as related to "the fishing problem" even if the other applications of it are much more obvious. The angler goes fishing. He uses various techniques and he has at most two fishing rods. He buys a…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
We consider the problem of motion of several rigid bodies immersed in a perfect compressible fluid. Using the method of convex integration we establish the existence of infinitely many weak solutions with {\it a priori} prescribed motion of…
Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions…
We derive analytical formulas for the wake and wave drag of a disturbance moving arbitrarily at the air-water interface. We show that, provided a constant velocity is reached in finite time, the unsteady surface displacement converges to…
We examine the motion of rigid, ellipsoidal swimmers subjected to a steady vortex flow in two dimensions. Numerical simulations of swimmers in a spatially periodic array of vortices reveal a range of possible behaviors, including trapping…
Consider a system of particles performing branching Brownian motion with negative drift $\mu = \sqrt{2 - \epsilon}$ and killed upon hitting zero. Initially there is one particle at $x>0$. Kesten showed that the process survives with…
We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…