相关论文: Radiating jump conditions in General Relativity

A definition of surface gravity at the apparent horizon of dynamical spherically symmetric spacetimes is proposed. It is based on a unique foliation by ingoing null hypersurfaces. The function parametrizing the hypersurfaces can be…

This article deals with the existence of hypersurfaces minimizing general shape functionals under certain geometric constraints. We consider as admissible shapes orientable hypersurfaces satisfying a so-called reach condition, also known as…

A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown…

We give an explicit estimate of the distance of a closed, connected, oriented and immersed hypersurface of a space form to a geodesic sphere and show that the spherical closeness can be controlled by a power of an integral norm of the…

The surface current method known in the theory of electromagnetic waves diffraction is generalized to be applied for the problems of diffraction radiation generated by a charged particle moving nearby an ideally-conducting screen in vacuum.…

We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…

This article experimentally investigates the exit dynamics of two different spheres i.e. a smooth sphere and a sphere with dimples at a constant speed. Employing high-speed experimental observations, the study investigates the key…

Given $2n$ unit equilateral triangles, there are finitely many ways to glue each edge to a partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the gluings that produce a topological sphere. As $n$ tends to…

Spreading of different types of fluid on substrates under an impressed force is an interesting problem. Here we study spreading of four fluids, having different hydrophilicity and viscosity on two substrates - glass and perspex, under an…

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…

Rough surfaces submerged in a liquid can remain almost dry if the liquid does not fully wet the roughness and gases are sustained in roughness grooves. Such partially dry surfaces can help reduce drag or enhance boiling. Gases sustained in…

The propagation of surface plasmons on a quantum plasma half-space in the absence of any external confinement is investigated. By means of Quantum Hydrodynamic Model in the electrostatic limit it is found that the equilibrium density…

The dissolution of porous materials in a flow field shapes the morphologies of many geologic landscapes. Identifying the dissolution front, the interface between the reactive and the unreactive regions in a dissolving medium, is a…

We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and…

The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…

We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity…

Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…

We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat's-eye…

We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are…

Using a framework based on the $1+3$ formalism we carry out a study on axially and reflection symmetric dissipative fluids, in the quasi--static regime. We first derive a set of invariantly defined "velocities", which allow for an…