Related papers: Error Analysis regarding the calculation of NLFF F…
It is a common practice in the solar physics community to test whether or not measured photospheric or chromospheric vector magnetograms are force-free, using the Maxwell stress as a measure. Some previous studies have suggested that…
Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…
This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the…
In this paper, we analyze the accuracy of gradient estimates obtained by linear interpolation when the underlying function is subject to bounded measurement noise. The total gradient error is decomposed into a deterministic component…
A new method for measuring the linewidth enhancement factor of a laser is proposed. It is based on frequency-modulated optical injection, combined with dual-frequency laser operation. The linewidth enhancement factor {\alpha} is deduced…
We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis-set representation (Fabian et al. WIREs Comput Mol Sci. 2019;e1412.…
Full-disk measurements of the solar magnetic field by the Helioseismic and Magnetic Imager (HMI) are often used for magnetic field extrapolations, but its limited spatial and spectral resolution can lead to significant errors. We compare…
The prior works on near-field target localization have mostly assumed ideal hardware models and thus suffer from two limitations in practice. First, extremely large-scale arrays (XL-arrays) usually face a variety of hardware impairments…
In this work we present TRFD, a derivative-free trust-region method based on finite differences for minimizing composite functions of the form $f(x)=h(F(x))$, where $F$ is a black-box function assumed to have a Lipschitz continuous…
In this paper, we propose and analyze the extrapolation method and asymptotically exact a posterior error estimate for eigenvalues of the Morley element. We establish an asymptotic expansion of eigenvalues, and prove an optimal result for…
Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
The Davis-Chandrasekhar-Fermi (DCF) method is widely used to indirectly estimate the magnetic field strength from the plane-of-sky field orientation. In this work, we present a set of 3D MHD simulations and synthetic polarization images…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models…
Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of interpolation points which conform to the computational domain $\Omega$. One of the requirements leading to approximation robustness is to place…
In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…
Classical approximation and learning methods are typically optimized for interpolation over a sampled domain {\Omega}, with no guarantees on their behavior in an extrapolation region {\Xi}, where small in-domain errors may amplify. We…
Exterior sound field interpolation is a challenging problem that often requires specific array configurations and prior knowledge on the source conditions. We propose an interpolation method based on Gaussian processes using a point source…
Possibilities in principle for satisfactory removal of the 180-azimuthal ambiguity in the transverse field of vector magnetograms and the extrapolation of magnetic fields independently of their position on the solar disk are shown. Revealed…