相关论文: Rigid Lid limit in shallow water over a flat botto…

We study a model describing the motion of the fluid in a lake, assuming inflow-outflow effects across the bottom, the porous coast and the inflows and outflows of rivers. We prove the global in time existence result for this model. The…

Steady swimming can be characterized as both periodic and stable. These characteristics are the very definition of limit cycles, and so we ask "Can we view swimming as a limit cycle?" In this paper we will find that the answer is "yes". We…

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…

A linear stability analysis is performed on a tilted parallel wake in a strongly stratified fluid at low Reynolds numbers. A particular emphasis of the present study is given to the understanding of the low-Froude-number mode observed by…

In this contribution we review a series of simple one dimensional lattice models that with an appropriate choice of parameters can account for various anomalous features of the behaviour of complex systems such as water. In particular, we…

Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations…

The dynamics of drop impact on solid surfaces can be changed significantly by tuning the elasticity of the solid. Most prominently, the substrate deformation causes an increase in the splashing threshold as compared to impact onto perfectly…

We consider a singular limit problem for the Navier-Stokes system of a rotating compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The limit problem is identified as the 2-D Navier-Stokes system in the…

A straightforward criterion to determine the limp model validity for porous materials is addressed here. The limp model is an "equivalent fluid" model which gives a better description of the porous behavior than the well known "rigid frame"…

We study the singular limit of a rotating compressible fluid described by a scaled barotropic Navier-Stokes system, where the Rossby number, the Mach number and the Froude number tend to 0 in a particular mutual rate while the Reynolds…

In the low-speed limit, a blunt ship modeled as two-dimensional semi-infinite body with a single corner can never be made waveless. This was the conclusion of the previous part of our work in Trinh et al. (2011), which focused on the Dagan…

In this paper the model for a highly viscous droplet sliding down an inclined plane is analyzed. It is shown that, provided the slope is not too steep, the corresponding moving boundary problem possesses classical solutions. Well-posedness…

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not…

We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier-Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain…

Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example when a ribbon has half a twist and is…

We revisit the classic problem of the stability of drops and jets held by surface tension, while regarding the compressibility of bulk fluids and spatial dimensions as free parameters. By mode analysis, it is shown that there exists a…

This paper studies a singular limit problem for a reduced model for compressible non-resistive MHD which was first introduced in \cite{Li-Sun_JDE, Li-Sun} in a two-dimensional setting. This system can also be related to a certain class of…

In this paper, we consider the high-Weissenberg number limit of a Voigt-regularized two-dimensional Oldroyd-B model for viscoelastic fluids. We first demonstrate that the Euler-Oldroyd-B system is both linearly and nonlinearly ill-posed in…

The dynamic behavior of the slip length in a fluid flow confined between atomically smooth surfaces is investigated using molecular dynamics simulations. At weak wall-fluid interactions, the slip length increases nonlinearly with the shear…

A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that…