Related papers: Slow divergence integral in regularized piecewise …

Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…

Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these strong capabilities remain only partially understood. A…

The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…

The aim of this paper is to provide a discussion on current directions of research involving typical singularities of 3D nonsmooth vector fields. A brief survey of known results is presented. The main purpose of this work is to describe the…

In piecewise-smooth differential systems, a hyperbolic limit cycle of a subsystem loses its structural stability if it grazes the switching manifold at a tangent point. Such a cycle is called a grazing loop and in this paper we investigate…

An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…

Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple…

It is well known that a k-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of k-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces,…

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

In this paper the statement of the second Bogolyubov's theorem on periodic solutions of smooth systems with small parameter is justified for discountinuous systems. It is assumed that the generating solution intersects the discontinuity…

The Minkowski function is a crucial tool used in the study of balanced domains and, more generally, quasi-balanced domains in several complex variables. If a quasi-balanced domain is bounded and pseudoconvex then it is well-known that its…

The classical Minkowski inequality implies that the volume of a bounded convex domain is controlled from above by the integral of the mean curvature of its boundary. In this note, we establish an analogous inequality without the convexity…

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…

We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide…