相关论文: Shape optimization of harmonic helicity in toroida…
Investigations of the inverse cascade of magnetic helicity are conducted with pseudospectral, three-dimensional direct numerical simulations of forced and decaying incompressible magnetohydrodynamic turbulence. The high-resolution…
Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective.…
Magnetic hopfions are localized magnetic solitons with non-zero 3D topological charge (Hopf index). Here I present an analytical calculation of the toroidal magnetic hopfion vector potential, emergent magnetic field, the Hopf index, and the…
We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference…
Topology optimization, a technique to determine where material should be placed within a predefined volume in order to minimize a physical objective, is used across a wide range of scientific fields and applications. A general application…
We investigate in isothermal MHD simulations the instability of toroidal magnetic fields resulting by the action of z-dependent differential rotation on a given axial field B^0 in a cylindrical enclosure where in particular the helicity of…
Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered.…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
Magnetic-ferroic ordering and magnetic-toroidal moments are essential concepts in molecular electronics and magnetics. The magnetic toroidal moment is critical in understanding new electronic states and their possible uses. This paper…
Ceramic is a material frequently used in industry because of its favorable properties. Common approaches in shape optimization for ceramic structures aim to minimize the tensile stress acting on the component, as it is the main driver for…
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…
The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The…
Current helicity quantifies the location of twisted and sheared non-potential structures in a magnetic field. We simulate the evolution of magnetic fields in the solar atmosphere in response to flux emergence and shearing by photospheric…
We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never…
The electromagnetic helicity of the free electromagnetic field and the static magnetic helicity are shown to be two different embodiments of the same physical quantity, the total helicity. The total helicity is the sum of two terms: a term…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
In this work we propose a method to perform optimization on manifolds. We assume to have an objective function $f$ defined on a manifold and think of it as the potential energy of a mechanical system. By adding a momentum-dependent kinetic…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…
We derive a new bound on the dimension of images of period maps of global pure polarized integral variations of Hodge structures with generic Hodge datum of level at least 3. When the generic Mumford-Tate domain of the variation is a period…