Related papers: Shape uncertainty quantification of Maxwell eigenv…
White paper: The aim of this work is to apply and analyze machine learning methods for uncertainty quantification of turbulence models. In this work we investigate the classical and data-driven variants of the eigenspace perturbation…
In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…
Modeling a single crystal of cuprate high-$T_c$ superconductor, such as $\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$, as a stack of intrinsic Josephson junctions, we formulate explicitly the cavity phenomenon of plasma oscillations and electromagnetic…
Continuum kinetic simulations are increasingly capable of resolving high-dimensional phase space with advances in computing. These capabilities can be more fully explored by using linear kinetic theory to initialize the self-consistent…
In this paper, we study an eigenvalue problem with piecewise constant coefficients on thin domains with Neumann boundary condition, and we analyze the asymptotic behavior of each eigenvalue as the domain degenerates into a certain…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the local extrinsic and intrinsic curvature. We show that the…
Evaluating structural uncertainties associated with seismic imaging and target horizons can be of critical importance for decision-making related to oil and gas exploration and production. An important breakthrough for industrial…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in…
We present a unified description of extremal metrics for the Laplace and Steklov eigenvalues on manifolds of arbitrary dimension using the notion of $n$-harmonic maps. Our approach extends the well-known results linking extremal metrics for…
With tangent angle perturbation approach the axial symmetry deformation of a spherical vesicle in large under the pressure changes is studied by the elasticity theory of Helfrich spontaneous curvature model.Three main results in axial…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
We investigate deformations of extremal near-horizon geometries in Einstein-Maxwell-Dilaton theory, including various topological terms, and also in D=11 supergravity. By linearizing the field equations and Bianchi identities over the…
The shape of the anisotropic velocity distribution function, beyond the realm of strict Maxwellians can play a significant role in determining the evolution of the Weibel instability dictating the dynamics of self-generated magnetic fields.…
The present paper deals with the interior solid-fluid interaction problem in harmonic regime with randomly perturbed boundaries. Analysis of the shape derivative and shape Hessian of vector- and tensor-valued functions is provided. Moments…
The stability characteristics of compressible spanwise-periodic open-cavity flows are investigated with direct numerical simulation and biglobal stability analysis for rectangular cavities with aspect ratios of $L/D=2$ and 6. This study…
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…