Related papers: Spectral Methods for capillary surfaces described …
The capillary time-step constraint is the dominant limitation on the applicable time-step in many simulations of interfacial flows with surface tension and, consequently, governs the execution time of these simulations. We propose a…
We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations \cite{Borchardt:2015rxa}. The advantages of our method are illustrated with the help of…
Nonlinear spectral problems arise across a range of fields, including mechanical vibrations, fluid-solid interactions, and photonic crystals. Discretizing infinite-dimensional nonlinear spectral problems often introduces significant…
We study evolution equations with non-self-adjoint generators, for example the convection-diffusion equation. Spectral expansions are not a reliable method of solving such equations, because they are so ill-conditioned. We introduce a new…
We propose a level set method to reconstruct unknown surfaces from point clouds, without assuming that the connections between points are known. We consider a variational formulation with a curvature constraint that minimizes the surface…
We study the Dirichlet problem associated to the equation for self-similar surfaces for graphs over the Euclidean plane with a disk removed. We show the existence of a solution provided the boundary conditions on the boundary circle are…
Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equations applicability for arbitrarily curved surface has been long…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
The unavailability of accurate boundary treatment methods for compressible Smoothed Particle Hydrodynamics (SPH) severely limits its ability to simulate flows in and around bodies. To this end, challenges specific to compressible flows with…
The Closest Point method, initially developed by Ruuth and Merriman, allows for the numerical solution of surface partial differential equations without the need for a parameterization of the surface itself. Surface quantities are embedded…
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication…
Existing numerical methods for modeling magnetization in thin type-II superconducting films have mostly been developed for flat films. This work introduces an efficient spectral method for axisymmetric magnetization problems involving…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
We introduce the point degree spectrum of a represented space as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on. The notion of point degree spectrum…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is…
We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. Here there are N identical sources that turn "on" and "off", and when "on" they generate fluid at unit rate into a buffer, which…
We present a framework for solving partial different equations on evolving surfaces. Based on the grid-based particle method (GBPM) [18], the method can naturally resample the surface even under large deformation from the motion law. We…
In this paper, we investigate topological modes of different physical systems defined on arbitrary two-dimensional curved surfaces. We consider the shallow water equations, inhomogeneous Maxwell's equations, Jackiw-Rebbi model and show how…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…