Change search
Link to record
Permanent link

Direct link
Publications (10 of 155) Show all publications
Raveendran, V., de Bonis, I., Cirillo, E. N. M. & Muntean, A. (2025). Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data. Quarterly of Applied Mathematics, 83(1), 19-57
Open this publication in new window or tab >>Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data
2025 (English)In: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485, Vol. 83, no 1, p. 19-57Article in journal (Refereed) Published
Abstract [en]

We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. We are interested in deriving rigorously the upscaled model equations and the corresponding effective coefficients for the case when the microscopic dynamics are linked to a particular choice of characteristic length and time scales that lead to an exploding nonlinear drift. The main mathematical difficulty lies in proving the two-scale compactness and strong convergence results needed for the passage to the homogenization limit. To cope with the situation, we use the concept of two-scale compactness with drift, which is similar to the more classical two-scale compactness result but it is defined now in moving coordinates. We provide as well a strong convergence result for the corrector function, starting this way the search for the order of the convergence rate of the homogenization process for our target nonlinear drift problem.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2025
Keywords
Homogenization, reaction-diffusion equations with large nonlinear drift, two-scale convergence with drift, strong convergence in moving coordinates, effective dispersion tensors for reactive flow in porous media
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-97991 (URN)10.1090/qam/1687 (DOI)001162782500001 ()2-s2.0-85213956275 (Scopus ID)
Funder
Swedish Research Council, 2018-03648
Available from: 2024-01-14 Created: 2024-01-14 Last updated: 2025-01-23Bibliographically approved
Lyons, R., Nika, G. & Muntean, A. (2024). A bound preserving energy stable scheme for a nonlocal Cahn--Hilliard equation. Comptes rendus. Mecanique
Open this publication in new window or tab >>A bound preserving energy stable scheme for a nonlocal Cahn--Hilliard equation
2024 (English)In: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234Article in journal (Refereed) Published
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-101481 (URN)
Funder
Carl Tryggers foundation , CTS 21:1656Knowledge Foundation, 2020-0152
Available from: 2024-08-27 Created: 2024-08-27 Last updated: 2024-10-31
Lyons, R., Muntean, A. & Nika, G. (2024). A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn-Hilliard Equation. Comptes rendus. Mecanique, 352, 239-250
Open this publication in new window or tab >>A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn-Hilliard Equation
2024 (English)In: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234, Vol. 352, p. 239-250Article in journal (Refereed) Published
Abstract [en]

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 special case of a previously derived and studied system of equations which describes phase separation in ternary mixtures. We prove the scheme is both energy stable and respects the analytical bounds of the solution. Furthermore, we present numerical demonstrations of the theoretical results using both the Flory-Huggins (FH) and Ginzburg-Landau (GL) free-energy potentials.

Place, publisher, year, edition, pages
Academie des Sciences, 2024
Keywords
Nonlocal Cahn-Hilliard equation, gradient flow, finite-volume method, bound preserving energy stable schemes
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-102607 (URN)10.5802/crmeca.265 (DOI)001382740900001 ()2-s2.0-85212864182 (Scopus ID)
Available from: 2025-01-03 Created: 2025-01-03 Last updated: 2025-01-03Bibliographically approved
Benes, M., Eden, M. & Muntean, A. (2024). Asymptotic analysis of a coupled ODE-PDE system arising from heterogeneous diffusion-reaction kinetics. Zeitschrift für angewandte Mathematik und Mechanik
Open this publication in new window or tab >>Asymptotic analysis of a coupled ODE-PDE system arising from heterogeneous diffusion-reaction kinetics
2024 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, ZAMM, ISSN 0044-2267Article in journal (Refereed) Epub ahead of print
Abstract [en]

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 coefficients and taking into account disparate diffusion-reaction time scales, including regularly as well as singularly perturbed problems. The ODE-PDE system is spatially dependent and is subjected to Robin-type boundary conditions. Such problems are used to model a variety of processes and phenomena such as combustion and exothermal chemical reactions. We will have a special look at the questions of the existence, uniqueness, boundedness, and the asymptotic limit of the microscale problem by applying the two-scale convergence and unfolding method. A numerical example illustrates both the expected behavior of the approximated solutions as well as the capability of the proposed upscaled models.

Place, publisher, year, edition, pages
John Wiley & Sons, 2024
National Category
Mathematical Analysis Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-102234 (URN)10.1002/zamm.202400181 (DOI)001367445100001 ()2-s2.0-85210730650 (Scopus ID)
Funder
EU, Horizon 2020, 101061956
Available from: 2024-11-17 Created: 2024-11-17 Last updated: 2024-12-19Bibliographically approved
Nika, G. & Muntean, A. (2024). Effective medium theory for second-gradient elasticity with chirality. Asymptotic Analysis, 139(1-2), 111-137
Open this publication in new window or tab >>Effective medium theory for second-gradient elasticity with chirality
2024 (English)In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576, Vol. 139, no 1-2, p. 111-137Article in journal (Refereed) Published
Abstract [en]

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 of the heterogeneities ℓ, the intrinsic lengths of the constituents ℓSG and ℓchiral, and the overall characteristic length of the domain L. Depending on the different scale interactions between ℓSG, ℓchiral, ℓ, and L we obtain either an effective Cauchy continuum or an effective second-gradient continuum. The working technique combines scaling arguments with the periodic homogenization asymptotic procedure. Both the passage to the homogenization limit and the unveiling of the correctors’ structure rely on a suitable use of the periodic unfolding operator.

Place, publisher, year, edition, pages
IOS Press, 2024
Keywords
Second-gradient elasticity, scale-size effects, partial scale separation, chirality, multi-continuum homogenization
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-98586 (URN)10.3233/ASY-241902 (DOI)001311138000005 ()2-s2.0-85201163551 (Scopus ID)
Funder
Knowledge Foundation, 2020-0152
Available from: 2024-02-18 Created: 2024-02-18 Last updated: 2024-10-07Bibliographically approved
Mellroth, E. & Muntean, A. (2024). Mathematics meets industry a day full of creativity and joy. In: : . Paper presented at 19th European Council for High Ability Conference Expanding Horizons: The Odyssey of Talents and Gift.
Open this publication in new window or tab >>Mathematics meets industry a day full of creativity and joy
2024 (English)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

On the mathematics meets industry day (MiMM) we gather mathematics enthusiasts from a wide range of competencies. Senior researchers, doctoral students, people from industry, university students as well as high school students attend the day, all with a huge interest of mathematics. Industries, both from Sweden and other countries, are invited to pose a real problem. To create a creative atmosphere the participants are given full freedom in their approach on the problems. We have organized this day yearly since 2017 and the evaluations gives proof that gifted people flourish when engaged in such open-ended opportunities. In addition, the one-day work of the participants give industry important input on the posed problems, and sometimes the problem is given a solution. An important result of the day is the perceived joy the participants express for coming together with like-minded individuals and opportunity for challenging thinking. In our presentation we will present guidelines on how to set up a day like this. We will also present a summary of the event’s evaluation based on the seven years the MiMM day has been running.

Keywords
Likeminded, challenges, mathematics, creativity
National Category
Mathematics Didactics
Identifiers
urn:nbn:se:kau:diva-101771 (URN)
Conference
19th European Council for High Ability Conference Expanding Horizons: The Odyssey of Talents and Gift
Available from: 2024-09-26 Created: 2024-09-26 Last updated: 2024-09-26
Alam, M., Muntean, A. & Raja Sekhar, G. P. (2024). Nonlinear biphasic mixture model: Existence and uniqueness results. European journal of applied mathematics (Print)
Open this publication in new window or tab >>Nonlinear biphasic mixture model: Existence and uniqueness results
2024 (English)In: European journal of applied mathematics (Print), ISSN 0956-7925, E-ISSN 1469-4425Article in journal (Refereed) Accepted
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-98944 (URN)
Available from: 2024-03-17 Created: 2024-03-17 Last updated: 2024-06-28
Alam, M., Muntean, A. & Sekhar, G. P. (2024). Non-linear biphasic mixture model: Existence and uniqueness results. European journal of applied mathematics (Print), 1-25
Open this publication in new window or tab >>Non-linear biphasic mixture model: Existence and uniqueness results
2024 (English)In: European journal of applied mathematics (Print), ISSN 0956-7925, E-ISSN 1469-4425, p. 1-25Article in journal (Refereed) Epub ahead of print
Abstract [en]

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 mixture theory is adopted for mass and momentum balance equations for a two-phase system. A main contribution of this study is we treat the physiological transport parameter (i.e., hydraulic resistivity) as anisotropic and heterogeneous, thus the governing system is strongly coupled and non-linear. We derived a weak formulation and then formulated the equivalent fixed-point problem. This enabled us to use the Galerkin method, and the classical results on monotone operators combined with the well-known Schauder and Banach fixed-point theorems to prove the existence and uniqueness of results.

Place, publisher, year, edition, pages
Cambridge University Press, 2024
Keywords
in-vitro tumour, biphasic mixture theory, hydraulic resistivity, weak solutions, fixed-point theory, 76Txx, 76Zxx
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-101885 (URN)10.1017/S0956792524000251 (DOI)001314795700001 ()2-s2.0-85204688905 (Scopus ID)
Available from: 2024-10-07 Created: 2024-10-07 Last updated: 2024-10-07Bibliographically approved
Lakkis, O., Muntean, A., Richardson, O. & Venkataraman, C. (2024). Parallel two-scale finite element implementation of a system with varying microstructure. GAMM Mitteilungen, 47(4), Article ID e202470005.
Open this publication in new window or tab >>Parallel two-scale finite element implementation of a system with varying microstructure
2024 (English)In: GAMM Mitteilungen, ISSN 0936-7195, Vol. 47, no 4, article id e202470005Article in journal (Refereed) Published
Abstract [en]

We propose a two-scale finite element method designed for heterogeneousmicrostructures. Our approach exploits domain diffeomorphisms between themicroscopic structures to gain computational efficiency. By using a convenientlyconstructed pullback operator, we are able to model the different microscopicdomains as macroscopically dependent deformations of a reference domain.This allows for a relatively simple finite element framework to approximatethe underlying system of partial differential equations with a parallel computa-tional structure. We apply this technique to a model problem where we focuson transport in plant tissues. We illustrate the accuracy of the implementationwith convergence benchmarks and show satisfactory parallelization speed-ups.We further highlight the effect of the heterogeneous microscopic structure onthe output of the two-scale systems. Our implementation (publicly available onGitHub) builds on the deal.II FEM library. Application of this techniqueallows for an increased capacity of microscopic detail in multiscale modeling,while keeping running costs manageable.

Place, publisher, year, edition, pages
John Wiley & Sons, 2024
Keywords
computational efficiency, finite elements, multiscale modeling, varying microstructures1 INTRODUCTIONModels involving transport and diffusion phenomena interacting at multiple scales (multiscale) are ubiquitous in thenatural sciences and engineering [52]. Multiscale modeling is a key tool for developing effective techniques to describethese phenomena, which may otherwise be computationally intractable. Specifically, assuming scale-separation in mod-els allows us to examine the interplay between processes active on vastly different length and time scales; defining, forexample, phenomena on macroscales and microscales [13, 22, 47, 48, 53]. In most practically relevant cases, the microscalesare active in the sense that they are hosting localized phase transitions described mathematically by moving interfaceswith a priori known or unknown velocities. The case of known interface velocities is both mathematically and computa-tionally well-understood (cf. e.g., [10]), while the case of unknown interface velocities is still a matter of concern; compare[11, 17, 44, 55] for some very recent asymptotic analysis results concerning closely related reaction-diffusion scenarioswhich arise in the context of reactive transport in porous media.Here, we consider a flow process that takes place on two distinct physical scales. In the simplest setting, we canidentify a macroscopic scale where a model governs the behavior of a (macroscopic) fluid in which averages over theThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided theoriginal work is properly cited.© 2024 The Authors. GAMM - Mitteilungen published by Wiley-VCH GmbH.GAMM - Mitteilungen. 2024;47:e202470005. wileyonlinelibrary.com/journal/gamm 1 of 18https://doi.org/10.1002/gamm.202470005
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-101668 (URN)10.1002/gamm.202470005 (DOI)2-s2.0-85206903463 (Scopus ID)
Funder
EU, Horizon Europe, Mod- CompShock ITNSwedish National Infrastructure for Computing (SNIC), 2020/9-178Swedish Research Council, 2018-03648National Academic Infrastructure for Supercomputing in Sweden (NAISS), 2023/22-1283
Available from: 2024-09-23 Created: 2024-09-23 Last updated: 2024-11-06Bibliographically approved
Lyons, R., Cirillo, E. N. M. & Muntean, A. (2024). Phase separation and morphology formation in interacting ternarymixtures under evaporation: Well-posedness and numerical simulation of a non-local evolution system. Nonlinear Analysis: Real World Applications, 77, Article ID 104039.
Open this publication in new window or tab >>Phase separation and morphology formation in interacting ternarymixtures under evaporation: Well-posedness and numerical simulation of a non-local evolution system
2024 (English)In: Nonlinear Analysis: Real World Applications, ISSN 1468-1218, Vol. 77, article id 104039Article in journal (Refereed) Published
Abstract [en]

We study a nonlinear coupled parabolic system with non-local drift terms modeling at the continuum level the inter-species interaction within a ternary mixture that allows the evaporation of one of the species. In the absence of evaporation, the proposed system coincides with the hydrodynamic limit of a stochastic interacting particle system of Blume–Capel-type driven by the Kawasaki dynamics. Similar governing dynamics are found in models used to study morphology formation in the design of organic solar cells, thin adhesive bands, and other applications. We investigate the well-posedness of the target system and present preliminary numerical simulations which incorporate ‘from the top’ evaporation into the model. We employ a finite volumes scheme to construct approximations of the weak solution and illustrate how the evaporation process can affect the shape and connectivity of the evolving-in-time morphologies

Place, publisher, year, edition, pages
Elsevier, 2024
Keywords
Phase separation, Coupled non-local parabolic system, Ternary mixture, Evaporation, Well-posedness, Numerical simulation
National Category
Metallurgy and Metallic Materials
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-97366 (URN)10.1016/j.nonrwa.2023.104039 (DOI)001123401400001 ()2-s2.0-85177884656 (Scopus ID)
Funder
Carl Tryggers foundation , CTS 21–1656
Available from: 2023-11-12 Created: 2023-11-12 Last updated: 2024-01-03Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-1160-0007

Search in DiVA

Show all publications