相关论文: Particle trajectories beneath small amplitude shal…

We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…

We derive the dispersion relation for linearized small-amplitude gravity waves for various choices of non-constant vorticity. To the best of our knowledge, this relation is only known explicitly in the case of constant vorticity. We provide…

In this paper, we prove the existence of two-dimensional, traveling, capillary-gravity, water waves with compactly supported vorticity. Specifically, we consider the cases where the vorticity is a $\delta$-function (a point vortex), or has…

The Rossby wave instability in astrophysical disks is as a potentially important mechanism for driving angular momentum transport in disks. We aim to understand this instability in an approximate three-dimensional disk model environment…

We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the…

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…

We investigate the motion of a suspended non-Brownian sphere past a fixed cylindrical or spherical obstacle in the limit of zero Reynolds number for arbitrary particle-obstacle aspect ratios. We consider both a suspended sphere moving in a…

Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfv\'en waves are…

In this paper we present a characterization of the symmetric rotational periodic gravity water waves of finite depth and without stagnation points in terms of the underlying flow. Namely, we show that such a wave is symmetric and has a…

We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…

We discuss the scaling laws for the flow generated in a viscous fluid by a wave propagating along a solid boundary. This has applications to the displacement of tiny objects on solids, under the effect of progressive surface waves and for…

Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…

We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…

We present a new numerical model to simulate settling trajectories of discretized individual or a mixture of particles of different geometrical shapes in a quiescent fluid and their flow trajectories in a flowing fluid. Simulations unveiled…

Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in the…

The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…

We study the dynamics of a small solid particle arising from the dewetting of a thin film on a curved substrate driven by capillarity, where mass transport is controlled by surface diffusion. We consider the case when the size of the…

The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales…

We study the phenomenon of the "walking droplet", by means of numerical fluid dynamics simulations using the Smoothed Particle Hydrodynamics numerical method. This phenomenon occurs when a millimetric drop is released on the surface of an…

We analyze the dynamics of a quantum particle in a one-dimensional bistable potential within the framework of Bohm's quantum mechanics. We give arguments that evidence the fallacy of certain claims found in the literature dealing with the…