Related papers: Deriving thin-film averaged equations using comput…
Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration…
In this paper, we introduce the concept of inner derivations of low-dimensional Zinbiel algebras and investigate their properties. The primary objective of this study is to develop an algorithm to characterize the inner derivations of any…
In the finite volume framework, a Lax-Wendrof type second-order flux solver for the compressible Navier-Stokes equations is proposed by utilizing a hyperbolic relaxation model. The flux solver is developed by applying the generalized…
The random deposition model must be enriched to reflect the variety of surface roughness due to some material characteristics of the film growing by vacuum deposition or sputtering. The essence of the computer simulation in this case is to…
Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures offer a more flexible…
In 1981, Foias, Guillop\'e and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier-Stokes equation. Such bounds are instructive in the numerical investigation of intermittency often observed in…
In this paper we review and systematize the mathematical theory on justification of sixth-order thin-film equations as reduced models for various fluid-structure interaction systems in which fluids are lubricating underneath elastic…
Because of the nonlocal properties of fractional operators, higher order schemes play more important role in discretizing fractional derivatives than classical ones. The striking feature is that higher order schemes of fractional…
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…
Algorithms of numeric (in exact arithmetic) deduction of analytical expressions, proposed and described by Shevchenko and Vasiliev (1993), are developed and implemented in a computer algebra code. This code is built as a superstructure for…
We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
This paper deals with the derivation of compressible two-phase flow models. We use a thin domain approximation of a two-layer configuration governed by the Navier-Stokes equations, following the works [H. B. Stewart and B. Wendroff, J.…
Via computation of a continuum dynamical model of the diffusion and electromigration, this paper demonstrates the feasibility of guiding the formation of the stripe composition patterns in the thin surface layers of the crystal alloy films.…
Model distillation has been a popular method for producing interpretable machine learning. It uses an interpretable "student" model to mimic the predictions made by the black box "teacher" model. However, when the student model is sensitive…
We examine the structural and dynamic properties of confined binary hard-sphere mixtures designed to mimic realizable colloidal thin films. Using computer simulations, governed by either Newtonian or overdamped Langevin dynamics, together…
This paper is concerned with model order reduction of parametric Partial Differential Equations (PDEs) using tree-based library approximations. Classical approaches are formulated for PDEs on Hilbert spaces and involve one single linear…
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be solved efficiently and accurately. Traditionally, these…
The presence of disorder in semiconductors can dramatically change their physical properties. Yet, models faithfully accounting for it are still scarce and computationally inefficient. We present a mathematical and computational model able…
The jet wiping process is a cost-effective coating technique that uses impinging gas jets to control the thickness of a liquid layer dragged along a moving strip. This process is fundamental in various coating industries (mainly in hot-dip…