Related papers: Shape uncertainty quantification of Maxwell eigenv…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
This work deals with theoretical and numerical aspects related to the behavior of the Steklov-Lam\'e eigenvalues on variable domains. After establishing the eigenstructure for the disk, we prove that for a certain class of Lam\'e…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
The behavior of Laplacian eigenfunctions in domains with branches is investigated. If an eigenvalue is below a threshold which is determined by the shape of the branch, the associated eigenfunction is proved to exponentially decay inside…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…
We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…
The fields in rectangular and circular waveguides are derived from Maxwell's equations by superposition of plane waves. Subsequently the results are applied to explain cavity modes. Interaction of the cavity modes with a charged particle…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
Recent advances in deep learning have led to its widespread adoption across diverse domains, including medical imaging. This progress is driven by increasingly sophisticated model architectures, such as ResNets, Vision Transformers, and…
The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong…
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…
Shape constraints enable us to reflect prior knowledge in regression settings. A unimodality constraint, for example, can describe the frequent case of a first increasing and then decreasing intensity. Yet, data shapes often exhibit…
The common feature of sheared flows of an ideal fluid and plasma in magnetic field is the Kelvin-Helmholtz instability. This instability is described by identical equations in mentioned two cases. The wave equation for the eigenmodes in the…
Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the…
Following the works by Wiegmann-Zabrodin, Elbau-Felder, Hedenmalm-Makarov, and others, we consider the normal matrix model with an arbitrary potential function, and explain how the problem of finding the support domain for the asymptotic…
A three dimensional small deformation theory is developed to examine the motion of a magnetic droplet in a uniform rotating magnetic field. The equations describing the droplet's shape evolution are derived using two different approaches -…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map…
The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental…