Related papers: Surface Current Optimization and Coil-Cutting Algo…
We are interested in the design of stellarators, devices for the production of controlled nuclear fusion reactions alternative to tokamaks. The confinement of the plasma is entirely achieved by a helical magnetic field created by the…
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation…
This work features the optimization of a Permanent Magnet Synchronous Motor using 2D nonlinear simulations in an Isogeometric Analysis framework. The rotor and stator designs are optimized for both geometric parameters and surface shapes…
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface $\Gamma \subset \mathbb{R}^3$ without boundary. This formulation leads to a coupled system of two second order scalar surface partial…
Stochastic computing (SC) is an emerging computing technique that promises high density, low power, and error tolerant solutions. In SC, values are encoded as unary bitstreams and SC arithmetic circuits operate on one or more bitstreams. In…
Design and modeling of a stellarator fusion reactor is a multidisciplinary effort that requires a tight integration between simulation of highly nonlinear multi-physics and representation of non-planar complex geometries. The critical…
In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…
The optimized stellarator is an attractive concept for which the averaged particle radial drift is zero, and the single particle loss can be significantly reduced. But for the reactor design, global physics such as turbulent transport also…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
Euler's elastica model has a wide range of applications in Image Processing and Computer Vision. However, the non-convexity, the non-smoothness and the nonlinearity of the associated energy functional make its minimization a challenging…
This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient)…
Cylindrical coordinates are often used in computational fluid dynamics, in particular, when one considers gas flow accreting onto a central object. Although the cylindrical coordinates have several advantages in describing rotation, they…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
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…
Purpose: Despite decades of collective experience, radiofrequency coil optimization for MR has remained a largely empirical process, with clear insight into what might constitute truly task-optimal, as opposed to merely 'good,' coil…
The time dependent Schrodinger equation inclusive of curvature effects is developed for a spinless electron constrained to motion on a toroidal surface and subjected to circularly polarized and linearly polarized waves in the microwave…
We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic…
We consider the surface Stokes equation on a smooth closed hypersurface in three-dimensional space. For discretization of this problem a generalization of the surface finite element method (SFEM) of Dziuk-Elliott combined with a Hood-Taylor…
In this work we describe a numerical optimization method for computing stationary MHD-equilibria. The newly developed code is based on a nonlinear force-free optimization principle. We apply our code to model the solar corona using synoptic…
A general approach is formulated to describe spontaneous surface current distribution in a chiral p-wave superconductor. We use the quasiclassical Eilenberger formalism in the Ricatti parametrization to describe various types of the…