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In this work we present a robust and accurate arbitrary order solver for the fixed-boundary plasma equilibria in toroidally axisymmetric geometries. To achieve this we apply the mimetic spectral element formulation presented in [56] to the…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
Because of their capacity-approaching performance and their complexity/latency advantages, spatially-coupled (SC) codes are among the most attractive error-correcting codes for use in modern dense data storage systems. SC codes are…
Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…
We present a technique to optimize the reflectivity of a surface while preserving its overall shape. The naive optimization of the mesh vertices using the gradients of reflectivity simulations results in undesirable distortion. In contrast,…
This paper optimizes the design and analysis of the mechanical test platform for the scientific probe module of the Cool Planet Imaging Coronagraph, which is the fifth part of the China Space Station survey Telescope. First, according to…
Constellation shaping is an energy-efficient strategy involving the transmission of lower-energy signals more frequently than higher-energy signals. Previous work has shown that shaping is particularly effective when used with coded…
An underlying structure in several sampling-based methods for continuous multi-robot motion planning (MRMP) is the tensor roadmap (TR), which emerges from combining multiple PRM graphs constructed for the individual robots via a tensor…
A magnetically dominated plasma driven by motions on boundaries at which magnetic field lines are anchored is forced to dissipate the work being done upon it, no matter how small the electrical resistivity. Numerical experiments have…
Neural fields are a highly effective representation across visual computing. This work observes that fitting these fields is greatly improved by incorporating spatial stochasticity during training, and that this simple technique can replace…
The method of solar magnetic field calibration for the filter-based magnetograph is normally the linear calibration method under weak-field approximation that cannot generate the strong magnetic field region well due to the magnetic…
The shape gradient is a local sensitivity function that provides the change in a figure of merit associated with a perturbation to the shape of the object. The shape gradient can be used for gradient-based optimization, sensitivity…
World models simulate environment dynamics from raw sensory inputs like video. However, using them for planning can be challenging due to the vast and unstructured search space. We propose a robust and highly parallelizable planner that…
We show that (i) any constrained polynomial optimization problem (POP) has an equivalent formulation on a variety contained in an Euclidean sphere and (ii) the resulting semidefinite relaxations in the moment-SOS hierarchy have the constant…
In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a…
We present, discuss and validate an adapted S-matrix formalism for an efficient, simplified treatment of stacked homogeneous periodically structured metasurfaces operated under normally incident plane wave excitation. The proposed formalism…
In this paper, we focus on large intelligent reflecting surfaces (IRSs) and propose a new codebook construction method to obtain a set of pre-designed phase-shift configurations for the IRS unit cells. Since the complexity of online…
In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. We derive a new necessary optimality…
The search for optimal configurations of pointsets, the most notable examples being the problems of Kepler and Thompson, have an extremely rich history with diverse applications in physics, chemistry, communication theory, and scientific…
This paper is concerned with the analysis and numerical analysis for the optimal control of first-order magneto-static equations. Necessary and sufficient optimality conditions are established through a rigorous Hilbert space approach.…