Adrian Muntean
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View article: Orthogonal Procrustes problem preserves correlations in synthetic data
Orthogonal Procrustes problem preserves correlations in synthetic data Open
This work introduces the application of the Orthogonal Procrustes problem to the generation of synthetic data. The proposed methodology ensures that the resulting synthetic data preserves important statistical relationships among features,…
View article: Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: simulation results
Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: simulation results Open
This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its s…
View article: 3D morphology formation in a mixture of three differently averse components
3D morphology formation in a mixture of three differently averse components Open
Film formation from solvent evaporation in polymer ternary solutions is relevant for several technological applications, such as the fabrication of organic solar cells. The performance of the final device will strongly depend on the intern…
View article: From Hallways to Highways: The Mathematics of Traffic
From Hallways to Highways: The Mathematics of Traffic Open
When designing schools and highways, engineers need to know how people might move through these structures. If they can accurately describe how crowds will react to their designs before they build the various structures, they can prepare f…
View article: Invariance properties of the solution operator for measure-valued semilinear transport equations
Invariance properties of the solution operator for measure-valued semilinear transport equations Open
We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is preserved, as well as absolute continuity with respect to Lebe…
View article: Mathematics for energy systems: Methods, modeling strategies, and simulation
Mathematics for energy systems: Methods, modeling strategies, and simulation Open
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior. …
View article: Asymptotic analysis of a coupled ODE‐PDE system arising from heterogeneous diffusion‐reaction kinetics
Asymptotic analysis of a coupled ODE‐PDE system arising from heterogeneous diffusion‐reaction kinetics Open
This contribution is concerned with the well‐posedness and homogenization of an ordinary differential equation (ODE) of Arrhenius‐type coupled with a doubly nonlinear parabolic partial differential equation (PDE) with rapidly oscillating c…
View article: A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation
A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation Open
We present a finite-volume based numerical scheme for a nonlocal Cahn–Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn–Hilliard equations. The equation of interest is a spec…
View article: Parallel two‐scale finite element implementation of a system with varying microstructure
Parallel two‐scale finite element implementation of a system with varying microstructure Open
We propose a two‐scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed …
View article: Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results
Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results Open
This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its s…
View article: Non-linear biphasic mixture model: Existence and uniqueness results
Non-linear biphasic mixture model: Existence and uniqueness results Open
This paper is concerned with the development and analysis of a mathematical model that is motivated by interstitial hydrodynamics and tissue deformation mechanics (poro-elasto-hydrodynamics) within an in-vitro solid tumour. The classical m…
View article: Precomputing approach for a two-scale phase transition model
Precomputing approach for a two-scale phase transition model Open
In this study, we employ analytical and numerical techniques to examine a phase transition model with moving boundaries. The model displays two relevant spatial scales pointing out to a macroscopic phase and a microscopic phase, interactin…
View article: Pattern formation in three-state systems: Towards understanding morphology formation in the presence of evaporation
Pattern formation in three-state systems: Towards understanding morphology formation in the presence of evaporation Open
Inspired by experimental evidence collected when processing thin films from ternary solutions made of two solutes, typically polymers, and one solvent, we computationally study the morphology formation of domains obtained in three-state sy…
View article: A hybrid approach to model reduction of Generalized Langevin Dynamics
A hybrid approach to model reduction of Generalized Langevin Dynamics Open
We consider a classical model of non-equilibrium statistical mechanics accounting for non-Markovian effects, which is referred to as the Generalized Langevin Equation in the literature. We derive reduced Markovian descriptions obtained thr…
View article: Thermo-Elasticity Problems with Evolving Microstructures
Thermo-Elasticity Problems with Evolving Microstructures Open
We consider the mathematical analysis and homogenization of a moving boundary problem posed for a highly heterogeneous, periodically perforated domain. More specifically, we are looking at a one-phase thermo-elasticity system with phase tr…
View article: A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn-Hilliard Equation
A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn-Hilliard Equation Open
We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a spec…
View article: Effective medium theory for second-gradient elasticity with chirality
Effective medium theory for second-gradient elasticity with chirality Open
We derive effective models for a heterogeneous second-gradient elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size …
View article: Tunable correlation retention: A statistical method for generating synthetic data
Tunable correlation retention: A statistical method for generating synthetic data Open
We propose a method to generate statistically representative synthetic data from a given dataset. The main goal of our method is for the created data set to mimic the inter--feature correlations present in the original data, while also off…
View article: Numerical Exploration of Nonlinear Dispersion Effects via a Strongly Coupled Two-scale System
Numerical Exploration of Nonlinear Dispersion Effects via a Strongly Coupled Two-scale System Open
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's law…
View article: Strongly Coupled Two-scale System with Nonlinear Dispersion: Weak Solvability and Numerical Simulation
Strongly Coupled Two-scale System with Nonlinear Dispersion: Weak Solvability and Numerical Simulation Open
We investigate a two-scale system featuring an upscaled parabolic dispersion-reaction equation intimately linked to a family of elliptic cell problems. The system is strongly coupled through a dispersion tensor, which depends on the soluti…
View article: Random walks and moving boundaries: Estimating the penetration of diffusants into dense rubbers
Random walks and moving boundaries: Estimating the penetration of diffusants into dense rubbers Open
For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front, giving a …
View article: Numerical explorations of solvent borne adhesives: a lattice-based approach to morphology formation
Numerical explorations of solvent borne adhesives: a lattice-based approach to morphology formation Open
The internal structure of adhesive tapes determines the effective mechanical properties. This holds true especially for blended systems, here consisting of acrylate and rubber phases. In this note, we propose a lattice-based model to study…
View article: Model reduction of Brownian oscillators: quantification of errors and long-time behavior
Model reduction of Brownian oscillators: quantification of errors and long-time behavior Open
A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in Colangeli et al (2022 J. Phys. A: Math. Theor. 55 505002), based on the Invariant Manifold method and on the Fluct…