Related papers: Currents and finite elements as tools for shape sp…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
A local current of particle density for scalar fields in curved background is constructed. The current depends on the choice of a two-point function. There is a choice that leads to local non-conservation of the current in a time-dependent…
As an alternative to solving of Poisson equation in Particle-in-Cell methods, a new construction of current density exactly satisfying continuity equation in finite differences is developed. This procedure called density decomposition is…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
We construct a branched center manifold in a neighborhood of a singular point of a $2$-dimensional integral current which is almost minimizing in a suitable sense. Our construction is the first half of an argument which shows the…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
Many active particles, both of biological and synthetic origin, can have a light controllable propulsion speed, a property that in biology is commonly referred to as photokinesis. Here we investigate directed transport of photokinetic…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…
Most of today's state-of-the-art methods for perspective shape from shading are modelled in terms of partial differential equations (PDEs) of Hamilton-Jacobi type. To improve the robustness of such methods w.r.t. noise and missing data,…
Studies of models of current flow behaviour in Electrical Impedance Tomography (EIT) have shown that the current density distribution varies extremely rapidly near the edge of the electrodes used in the technique. This behaviour imposes…
In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous…
Surface sensitive electric current measurements are important experimental tools poorly corroborated by theoretical models. We show that the drift-diffusion equations offer a framework for a consistent description of such experiments. The…
We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schr\"odinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The…
We study two actions of a stochastic flow $\varphi_t$ on the space of $0-$currents $T$ of a differentiable manifold $M$. In particular, we give conditions on a current $T$ to be invariant under these actions. Also, we apply our results to…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…