相关论文: Shape optimization of harmonic helicity in toroida…

We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations…

Toroidal vortex is a kind of novel and exotic structured light with potential applications in photonic topology and quantum information. Here, we present the study on high harmonic generation (HHG) from the interaction of the intense…

This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape which minimizes a certain cost…

Magnetic droplets obtained by induced phase separation in a magnetic colloid show a large variety of shapes when exposed to an external field. However, the description of shapes is often limited. Here we formulate an algorithm based on…

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

The polarization state of light plays a central role in strong-field light--matter interactions and is widely used to probe electronic structure in solids via high-order harmonic generation (HHG). In particular, helicity-resolved HHG has…

We recently proposed a method to calculate the relative magnetic helicity in a finite volume for a given magnetic field which however required the flux to be balanced separately on all the sides of the considered volume. In order to allow…

We develop a statistically robust framework for reconstructing metal--semiconductor contact regions using topological gradients. The inverse problem is formulated as the identification of an unknown contact region from boundary measurements…

In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its…

Helical structures are ubiquitous in nature and engineering, ranging from DNA molecules to plant tendrils, from sea snail shells to nanoribbons. While the helical shapes in natural and engineered systems often exhibit nearly uniform radius…

We use holography to derive effective theories of fluctuations in spontaneously broken phases of systems with finite temperature, chemical potential, magnetic field and momentum relaxation in which the order parameters break translations.…

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…

Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…

We investigate the existence of magnetohydrostatic equilibria for topologically complex magnetic fields. The approach employed is to perform ideal numerical relaxation experiments. We use a newly-developed Lagrangian relaxation scheme that…

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

We study the optimal domain for the Hardy operator considered with values in a rearrangement invariant space. In particular, this domain can be represented as the space of integrable functions with respect to a vector measure defined on a…

Tight tolerances have been a leading driver of cost in recent stellarator experiments, so improved definition and control of tolerances can have significant impact on progress in the field. Here we relate tolerances to the shape gradient…

We examine the relationship between magnetic flux generation, taken as an indicator of large-scale dynamo action, and magnetic helicity, computed as an integral over the dynamo volume, in a simple dynamo. We consider dynamo action driven by…

The surface Hamiltonian for a spin zero particle that is pinned to a surface by letting the thickness of a layer surrounding the surface go to zero -- assuming a strong normal force -- is constructed. The new approach we follow to achieve…