Related papers: Dimensional regularization applied to nuclear matt…
We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is…
Correlations play a crucial role in the nuclear many-body problem. We give an overview of recent developments in nuclear structure theory aiming at the description of these interaction-induced correlations by unitary transformations. We…
We show how to use dimensional regularization to determine, within the Arnowitt-Deser-Misner canonical formalism, the reduced Hamiltonian describing the dynamics of two gravitationally interacting point masses. Implementing, at the third…
Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired…
We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
A simple class of unitary renormalization group transformations that force hamiltonians towards a band-diagonal form produce few-body interactions in which low- and high-energy states are decoupled, which can greatly simplify many-body…
This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularisations of…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
In this article, we develop and present a novel regularization scheme for ill-posed inverse problems governed by nonlinear time-dependent partial differential equations (PDEs). In our recent work, we introduced a bi-level regularization…
Ring artifacts in computed tomography images, arising from the undesirable responses of detector units, significantly degrade image quality and diagnostic reliability. To address this challenge, we propose a dual-domain regularization model…
We develop a relativistic mean field (RMF) description of deformed nuclei with the pairing correlations in the BCS approximation. The treatment of the pairing correlations for nuclei with the Fermi surface being close to the threshold of…
We reconsider the renormalization of scalar mass and point out that the quantum correction to the physical observable, as opposed to the bare parameter, of a renormalizable operator, is technically insensitive to ultraviolet physics and…
The problem of ultraviolet divergences is analysed in the quantum field theory. It was found that it has common roots with the problem of cosmological singularity. In the context of fibre bundles the second quantization method is…
The multigroup neutron diffusion equations are often used to model the neutron density at the nuclear reactor core scale. Classically, these equations can be recast in a mixed variational form. This chapter presents an adaptive mesh…
Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
Due to an accidentally large $s$-wave scattering length, in a relatively wide range of energy, neutrons are approximately described by the nonrelativistic conformal field theory of unitarity fermions, perturbed by one relevant and an…
The Lip-field approach is a new regularization method for softening material material models. It was presented first in a previous paper providing one-dimensional simulations for damage and plasticity. The present paper focuses on a…
We study the regularity of solutions of elliptic second order boundary value problems on a bounded domain $\Omega$ in $\mathbb R^3$. The coefficients are not necessarily continuous and the boundary conditions may be mixed, i.e. Dirichlet on…