相关论文: Willmore Flow of planar networks

Flow observables in heavy-ion reactions at incident energies up to about 1 GeV per nucleon have been shown to be very useful for investigating the reaction dynamics and for determining the parameters of reaction models based on transport…

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behaviour. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence - a unique, chaotic…

Different variants of hybrid kinetic-fluid models are considered for describing the interaction of a bulk fluid plasma obeying MHD and an energetic component obeying a kinetic theory. Upon using the Vlasov kinetic theory for energetic…

In addition to providing high-profile successes in computer vision and natural language processing, neural networks also provide an emerging set of techniques for scientific problems. Such data-driven models, however, typically ignore…

The main goal of this paper is to present results of comparison study for the level set and direct Lagrangian methods for computing evolution of the Willmore flow of embedded planar curves. To perform such a study we construct new numerical…

This note concerns a nonlinear ill-posedness of the Prandtl equation and an invalidity of asymptotic boundary-layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear…

This paper is concerned with diffuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards…

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is…

The Landau-Lifshitz fluctuating hydrodynamics is used to study the statistical properties of the linearized Kolmogorov flow. The relative simplicity of this flow allows a detailed analysis of the fluctuation spectrum from near equilibrium…

We investigate the effect of polymer additives on a two-dimensional Kolmogorov flow at very low Reynolds numbers by direct numerical simulations of the Oldroyd-B viscoelastic model. We find that above the elastic instability threshold the…

We consider a general stable flow problem in a directed and capacitated network, where each vertex has a strict preference list over the incoming and outgoing edges. A flow is stable if no group of vertices forming a path can mutually…

We show the short-time existence and uniqueness of solutions for the motion of an evolving hypersurface in contact with a solid container driven by volume-preserving mean curvature flow (MCF) taking line tension effects on the boundary into…

We derive general conditions of slip of a fluid on the boundary. Under these conditions the velocity of the fluid on the immovable boundary is a function of the normal and tangential components of the force acting on the surface of the…

Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…

In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…

In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock past a curved wedge for the steady full Euler equations in an important physical regime, which form a nonlinear system of…

The elastic flow, which is the $L^2$-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are…

The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual based pore scale network modeling method…

We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the…