Related papers: An improved current potential method for fast comp…
Boundary integral equation methods are widely used in the solution of many partial differential equations. The kernels that appear in these surface integrals are nearly singular when evaluated near the boundary, and straightforward…
This study presents the design, simulation, and experimental validation of a novel multimodal concentric surface coil for MR imaging, developed to achieve higher B1 field efficiency while maintaining low SAR for enhanced imaging…
In recent years many efforts have been undertaken to simplify coil designs for stellarators due to the difficulties in fabricating non-planar coils. The FOCUS code removes the need for a winding surface and represents the coils as arbitrary…
With the advent of multi-coil imaging and compressed sensing, a number of model based reconstruction algorithms have been created. They incorporate a multitude of different regularization functions based on physics, observed phenomenology,…
A new code for computing fully general relativistic solutions of strongly magnetized rapidly rotating compact stars is developed as a part of the COCAL (Compact Object CALculator) code. The full set of Einstein's equations, Maxwell's…
We present a new coil design paradigm for magnetic confinement in stellarators. Our approach directly optimizes coil shapes and coil currents to produce a vacuum quasi-symmetric magnetic field with a target rotational transform on the…
An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the…
The thesis explores calculating tunneling current densities between planar conducting electrodes in an STM. It considers factors like bias voltages and the separation between electrodes, using Fermi energy and work functions. Pauli blocking…
In fusion reactor design, steels under consideration for the blanket are ferromagnetic, so the steel's effect on the plasma physics must be examined. For efficient calculation of these fields, we can exploit the fact that the magnetic…
We present a fundamentally new regularization method for the solution of the Fredholm integral equation of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method…
We propose a regularization-based deblurring method that works efficiently for galaxy images. The spatial resolution of a ground-based telescope is generally limited by seeing conditions and much worse than space-based telescopes. This…
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization.…
Predictive modeling of stellarator plasmas is crucial for advancing nuclear fusion energy, yet it faces unique computational difficulties. One of the main challenges is accurately simulating the dynamics of specific particle species that…
Tikhonov regularization is one of the most commonly used methods of regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to…
The method of regularised stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard…
It is shown that the magnetic-field coils of a stellarator can, at least in principle, be substantially simplified by the use of permanent magnets. Such magnets cannot create toroidal magnetic flux but they can be used to shape the plasma…
A new stellarator coil design code is introduced that optimizes the position and winding pack orientation of finite-build coils. The new code, called FOCUSADD, performs gradient-based optimization in a high-dimensional, non-convex space.…
Many problems in fluid dynamics are effectively modeled as Stokes flows - slow, viscous flows where the Reynolds number is small. Boundary integral equations are often used to solve these problems, where the fundamental solutions for the…
An optimized stellarator at finite plasma beta is realized by single-stage optimization of simply modifying the coil currents of the Compact Stellarator with Simple Coils (CSSC)[Yu et al., J. Plasma Physics 88,905880306 (2022)]. The CSSC is…
In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…