Related papers: A general method to compute numerical dispersion e…
In this paper, we design and analyze a novel spectral method for the subdiffusion equation. As it has been known, the solutions of this equation are usually singular near the initial time. Consequently, direct application of the traditional…
There is today a growing need to accurately model the angular scattering response of metasurfaces for optical analog processing applications. However, the current metasurface modeling techniques are not well suited for such a task since…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
Clustering analysis of functional data, which comprises observations that evolve continuously over time or space, has gained increasing attention across various scientific disciplines. Practical applications often involve functional data…
Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of…
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
In this work, we present a novel analytical model for tracer dispersion in laminar flow through porous media. Based on a straightforward physical argument, it describes the generic behavior of dispersion over a wide range of Peclet numbers…
We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
Science students must deal with the errors inherent to all physical measurements and be conscious of the need to expressvthem as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic.…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…