相关论文: New method to design stellarator coils without the…

Uniform magnetic field generation is one of the key issues in many physical applications; such as magnetic resonance imaging, magnetic probs etc. There are many ways to obtain highly homogeneous fields. For instance, ellipsoidal bodies -…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

A Converse KAM method for 3D vector fields, establishing regions through which pass no invariant 2-tori transverse to a given direction field, is tested on some helical perturbations of an axisymmetric magnetic field in toroidal geometry.…

Advanced stellarators are typically optimized in two stages. The plasma equilibrium is optimized first, followed by the design of coils/permanent magnets. However, the coils/permanent magnets in the second stage may become too complex to…

We describe a general family of curved-crease folding tessellations consisting of a repeating "lens" motif formed by two convex curved arcs. The third author invented the first such design in 1992, when he made both a sketch of the crease…

Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…

Adaptable, low-cost, coils designed by carefully selecting the arrangements and geometries of simple primitive units are used to generate magnetic fields for diverse applications. These extend from magnetic resonance and fundamental physics…

The confinement of guiding center trajectories in a stellarator is determined by the variation of the magnetic field strength $B$ in Boozer coordinates $(r, \theta, \varphi)$, but $B(r,\theta,\varphi)$ depends on the flux surface shape in a…

We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…

Hybrid magnetic shields with both active field generating components and high-permeability magnetic shielding are increasingly needed for a variety of technologies and experiments that require precision-controlled magnetic field…

Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane…

Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions…

Modeling the Scape-off layer (SOL) of stellarator fusion devices is challenging due to the complicated magnetic topology, requiring numerical tools to solve transport equations for realistic geometries. Previously the flux coordinate…

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having…

We describe an improvement on the magnetic scalar potential approach to the design of an electromagnet, which incorporates the need to wind the coil as a helix. Any magnetic field that can be described by a magnetic scalar potential is…

We set out the theory and discretization scheme for a new finite-element computer code, written specifically for the simulation of maser sources. The code was used to compute fractional inversions at each node of a 3-D domain for a range of…

Stellarators are a prospective class of fusion-based power plants that confine a hot plasma with three-dimensional magnetic fields. Typically framed as a PDE-constrained optimization problem, stellarator design is a time-consuming process…

The design of turbulence optimized stellarators has so far relied on three-dimensional equilibrium codes such as VMEC in order to find the minimum of a given objective function. In this work, we propose a complimentary approach based on the…

We consider the holographic computation of two dimensional conformal field theory partition functions on non-orientable surfaces. We classify the three dimensional geometries that give bulk saddle point contributions to the partition…

We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…