Related papers: Single-stage gradient-based stellarator coil desig…
The two-dimentional (2D) separatrix shaping plays a crucial role in the confinement of the Field Reversed Configuration (FRC), and the magnetic coils serve as an effective means for its control. In this work we develop a method to optimize…
Achieving stable, high-quality quantum dots has proven challenging within device architectures rooted in conventional solid-state device fabrication paradigms. In fact, these are grappled with complex protocols in order to balance ease of…
Single-site Markov Chain Monte Carlo (MCMC) is a variant of MCMC in which a single coordinate in the state space is modified in each step. Structured relational models are a good candidate for this style of inference. In the single-site…
Existing gradient coding schemes introduce identical redundancy across the coordinates of gradients and hence cannot fully utilize the computation results from partial stragglers. This motivates the introduction of diverse redundancies…
A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and…
In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…
We describe a simple way to drive an actuator, comprising a superconducting coil moving in a static magnetic field, at a quasi-uniform velocity. The main objective is to avoid oscillations in this system with low damping, as they undermine…
This paper presents a proximal-point-based catalyst scheme for simple first-order methods applied to convex minimization and convex-concave minimax problems. In particular, for smooth and (strongly)-convex minimization problems, the…
The separation between the last closed flux surface of a plasma and the external coils that magnetically confine it is a limiting factor in the construction of fusion-capable plasma devices. This plasma-coil separation must be large enough…
In this work we consider the problem of optimizing a stellarator subject to hard constraints on the design variables and physics properties of the equilibrium. We survey current numerical methods for handling these constraints, and…
Stellarators are generically small current and low plasma beta ($\beta= p/B^2\ll1$) devices. Often the construction of vacuum magnetic fields with good magnetic surfaces is the starting point for an equilibrium calculation. Although in…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
We study the control by electromagnetic fields of molecular alignment and orientation, in a linear, rigid rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the…
In this self-contained document, we aim to present the basic theoretical building blocks to understand modeling of stellarator magnetic fields, some of the challenges associated with modeling, and optimization for designing stellarators. As…
There is currently no agreed-upon methodology for characterizing a stellarator magnetic field geometry, and yet modern stellarator designs routinely attain high levels of magnetic-field quasi-symmetry through careful flux-surface shaping.…
The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in…
We apply topological methods to better understand how the magnetic field in the stellarator edge can be diverted away from the confined region. Our primary method is calculating the winding numbers of closed contours, which gives…
To better understand the dependence of the magnetic field structure in the plasma edge on the plasma boundary shape, in the context of X-point and island divertor designs, we define and develop a class of stellarators called umbilic…
We study a stochastic anchored gradient scheme, namely HalpernSGD, which combines the classical Halpern iteration for finding a minimizer of a convex and $L$-smooth objective function with a stochastic {first-order} oracle. The algorithm is…
It is well-known that the reparameterisation gradient estimator, which exhibits low variance in practice, is biased for non-differentiable models. This may compromise correctness of gradient-based optimisation methods such as stochastic…