相关论文: Feeble fish in time-dependent waters and homogeniz…
As avid anglers we were always interested in the survival chances of fish in turbulent oceans. This paper addresses this question mathematically. We show that a fish with bounded aquatic locomotion speed can reach any point in the ocean if…
The aim of the paper is to extend the model of "fishing problem". The simple formulation is following. The angler goes to fishing. He buys fishing ticket for a fixed time. There are two places for fishing at the lake. The fishes are caught…
We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is…
In this paper we study the locomotion of a shape-changing body swimming in a two-dimensional perfect fluid of infinite extent. The shape-changes are prescribed as functions of time satisfying constraints ensuring that they result from the…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
In the paper by D.~Burago, S.~Ivanov and A.~Novikov, "A survival guide for feeble fish", it has been shown that a fish with limited velocity can reach any point in the (possibly unbounded) ocean provided that the fluid velocity field is…
We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…
The paper studies homogenization problem for a non-autonomous parabolic equation with a large random rapidly oscillating potential in the case of one dimensional spatial variable. We show that if the potential is a statistically homogeneous…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and…
We study the homogenization of a $G$-equation which is advected by a divergence free stationary vector field in a general ergodic random environment. We prove that the averaged equation is an anisotropic deterministic G-equation and we give…
Dynamic network flows, sometimes called flows over time, extend the notion of network flows to include a transit time for each edge. While Ford and Fulkerson showed that certain dynamic flow problems can be solved via a reduction to static…
We consider the 1D viscous Burgers equation with a control localised in a finite interval. It is proved that, for any $\varepsilon>0$, one can find a time $T$ of order $\log\varepsilon^{-1}$ such that any initial state can be steered to the…
Description of tides is based on the form of dependence of the geometric lag on the tidal frequency. Some authors assume the lag angle to be constant, others set it to be linear in the frequency. The actual dependence of the lag on the…
We study the fluid dynamics of two fish-like bodies with synchronised swimming patterns. Our studies are based on two-dimensional simulations of viscous incompressible flows. We distinguish between motion patterns that are externally…
We address the problem of controlling a dynamical system governing the motion of a 3D weighted shape changing body swimming in a perfect fluid. The rigid displacement of the swimmer results from the exchange of momentum between prescribed…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed has to be paid with a loss of fidelity. Here we quantify the trade-off…
We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier-Stokes-Fourier system consisting of equation of continuity, momentum balance, entropy…