相关论文: Variational worn stones
For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…
In the study of low-speed or low-Froude flows of a potential gravity-driven fluid past a wave-generating object, the traditional asymptotic expansion in powers of the Froude number predicts a waveless free-surface at every order. This is…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
The fluid motion produced by a periodic array of identical, axisymmetric, thin-cored vortex rings is investigated. It is well known that such an array moves uniformly without change of shape or form in the direction of the central axis of…
We provide short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. The boundary behaviour is precisely described. Presented results may be considered as a complement or a generalization of the…
We derive the equations of motion for the dynamics of a porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
In this note we investigate the asymptotic behavior of plane shear thickening fluids around a bounded obstacle. Different from the Navier-Stokes case considered by Gilbarg-Weinberger in \cite{GW1978}, where the good structure of the…
The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a…
We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium…
Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single…
We perform one of the first studies into the nonlinear evolution of tidally excited inertial waves in a uniformly rotating fluid body, exploring a simplified model of the fluid envelope of a planet (or the convective envelope of a…
We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of…
The sedimentation of a spherical particle in an elastoviscoplastic fluid in proximity of a flat wall is investigated by direct numerical simulations. The governing equations under inertialess conditions are solved by the finite element…
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
We consider a one-parameter family of strictly convex hypersurfaces in $\mathbb{R}^{n+1}$ moving with speed $- K^\alpha \nu$, where $\nu$ denotes the outward-pointing unit normal vector and $\alpha \geq \frac{1}{n+2}$. For $\alpha >…
A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of…
The variational theory of the perfect fluid with an intrinsic hypermomentum is developed. The Lagrangian density of such fluid is stated and the equations of motion of the fluid and the evolution equation of the hypermomentum tensor are…
The existence of a crumpled phase for self-avoiding elastic surfaces was postulated more than three decades ago using simple Flory-like scaling arguments. Despite much effort, its stability in a microscopic environment has been the subject…