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Publications (10 of 149) Show all publications
Nika, G. & Muntean, A. (2024). Effective medium theory for second-gradient elasticity with chirality. Asymptotic Analysis
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 1875-8576Article in journal (Refereed) Accepted
Place, publisher, year, edition, pages
IOS Press, 2024
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-98586 (URN)
Funder
Knowledge Foundation, 2020-0152
Available from: 2024-02-18 Created: 2024-02-18 Last updated: 2024-03-11Bibliographically approved
Raveendran, V., de Bonis, I., Cirillo, E. N. M. & Muntean, A. (2024). Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data. Quarterly of Applied Mathematics
Open this publication in new window or tab >>Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data
2024 (English)In: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485Article in journal (Refereed) Epub ahead of print
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), 2024
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 ()
Funder
Swedish Research Council, 2018-03648
Available from: 2024-01-14 Created: 2024-01-14 Last updated: 2024-03-08Bibliographically approved
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: 2024-04-02
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
Lyons, R., Muntean, S. A., Cirillo, E. N. .. & Muntean, A. (2023). A Continuum Model for Morphology Formation from Interacting Ternary Mixtures: Simulation Study of the Formation and Growth of Patterns. Physica D: Non-linear phenomena, 453, Article ID 133832.
Open this publication in new window or tab >>A Continuum Model for Morphology Formation from Interacting Ternary Mixtures: Simulation Study of the Formation and Growth of Patterns
2023 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 453, article id 133832Article in journal (Refereed) Published
Abstract [en]

Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target system is derived in the literature as the rigorous hydrodynamic limit of a suitably scaled interacting particle system of Blume–Capel–type driven by Kawasaki dynamics. The system describes in a rather implicit way the interaction within a ternary mixture that is the macroscopic counterpart of a mix of two populations of interacting solutes in the presence of a background solvent. Our discussion is based on the qualitative behavior of numerical simulations of finite volume approximations of smooth solutions to our system and their quantitative postprocessing in terms of two indicators (correlation and structure factor calculations). Our results show many similar qualitative features (e.g. general shape and approximate coarsening rates) which have been observed in previous works on the stochastic Blume–Capel dynamics with three interacting species. The properties of the obtained morphologies (shape, connectivity, and so on) can play a key role in, e.g., the design of the active layer for efficient organic solar cells.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Continuum model, Interacting ternary mixture, Blume–Capel model with Kawasaki dynamics, Phase separation, Morphology formation, Domain growth, Numerical simulation
National Category
Other Physics Topics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-95685 (URN)10.1016/j.physd.2023.133832 (DOI)001109878200001 ()2-s2.0-85164729079 (Scopus ID)
Funder
Carl Tryggers foundation , 21:1656Swedish National Space Board, 174/19Knut and Alice Wallenberg Foundation, 2016.0059
Available from: 2023-06-25 Created: 2023-06-25 Last updated: 2023-12-22Bibliographically approved
Setta, M., Kronberg, V. C. .., Muntean, S. A., Moons, E., van Stam, J., Cirillo, E. N. .., . . . Muntean, A. (2023). A mesoscopic lattice model for morphology formation in ternary mixtures with evaporation. Communications in nonlinear science & numerical simulation, 119, Article ID 107083.
Open this publication in new window or tab >>A mesoscopic lattice model for morphology formation in ternary mixtures with evaporation
Show others...
2023 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 119, article id 107083Article in journal (Refereed) Published
Abstract [en]

We develop a mesoscopic lattice model to study the morphology formation in inter-acting ternary mixtures with the evaporation of one component. As concrete potentialapplication of our model, we wish to capture morphologies as they are typically arisingduring the fabrication of organic solar cells. In this context, we consider an evaporatingsolvent into which two other components are dissolved, as a model for a 2-componentcoating solution that is drying on a substrate. We propose a 3-spins dynamics to describethe evolution of the three interacting species. As main tool, we use a Monte CarloMetropolis-based algorithm, with the possibility of varying the system’s temperature,mixture composition, interaction strengths, and evaporation kinetics. The main novelty isthe structure of the mesoscopic model – a bi-dimensional lattice with periodic boundaryconditions, divided into square cells to encode a mesoscopic range interaction amongthe units. We investigate the effect of the model parameters on the structure of theresulting morphologies. Finally, we compare the results obtained with the mesoscopicmodel with corresponding ones based on an analogous lattice model with a short rangeinteraction among the units, i.e. when the mesoscopic length scale coincides with themicroscopic length scale of the lattice.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Concrete mixtures, Crystal lattices, Morphology, Organic solar cells, Superconducting materials, Coating solution, Interacting species, Lattice models, Mesoscopic lattice model, Mesoscopic modeling, Mesoscopics, Metropolis algorithms, Morphology formation, System temperature, Ternary mixtures, Evaporation
National Category
Condensed Matter Physics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-93041 (URN)10.1016/j.cnsns.2023.107083 (DOI)000921248500001 ()2-s2.0-85145774625 (Scopus ID)
Funder
Karlstad UniversitySwedish National Infrastructure for Computing (SNIC), 2020/9-178+10-94, 2022/22-1171Swedish National Space Board, 174/19Knut and Alice Wallenberg Foundation, 2019.0059Swedish Research Council, 2018-03648
Available from: 2023-01-23 Created: 2023-01-23 Last updated: 2023-02-23Bibliographically approved
Nepal, S., Wondmagegne, Y. & Muntean, A. (2023). Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants. Applied Mathematics and Computation, 442, Article ID 127733.
Open this publication in new window or tab >>Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants
2023 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 442, article id 127733Article in journal (Refereed) Published
Abstract [en]

We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with the backward Euler method for the time discretization. Besides dealing with the existence and uniqueness of solution to the fully discrete problem, we assume sufficient regularity for the solution to the target moving boundary problem and derive a a priori error estimates for the mass concentration of the diffusants, and respectively, for the position of the moving boundary. Our numerical results illustrate the obtained theoretical order of convergence in physical parameter regimes.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Moving-boundary problem, Finite element approximation, Fully discrete approximation, A priori error estimate
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-92518 (URN)10.1016/j.amc.2022.127733 (DOI)000923199000001 ()2-s2.0-85144575490 (Scopus ID)
Funder
Swedish Research Council, 018-03648Knowledge Foundation, 019-021
Available from: 2022-11-20 Created: 2022-11-20 Last updated: 2024-03-01Bibliographically approved
Thieu, T. K., Muntean, A. & Melnik, R. (2023). Coupled stochastic systems of Skorokhod type: Well-posedness of a mathematical model and its applications. Mathematical methods in the applied sciences, 46(6), 7368-7390
Open this publication in new window or tab >>Coupled stochastic systems of Skorokhod type: Well-posedness of a mathematical model and its applications
2023 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 46, no 6, p. 7368-7390Article in journal (Refereed) Published
Abstract [en]

Population dynamics with complex biological interactions, accounting for uncertainty quantification, are critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the corresponding problems faces the challenge that the corresponding stochastic processes should, in most cases, be considered in bounded domains. We propose a model based on a coupled system of reflecting Skorokhod-type stochastic differential equations with jump-like exit from a boundary. The setting describes the population dynamics of active and passive populations. As main working techniques, we use compactness methods and Skorokhod's representation of solutions to SDEs posed in bounded domains to prove the well-posedness of the system. This functional setting is a new point of view in the field of modeling and simulation of population dynamics. We provide the details of the model, as well as representative numerical examples, and discuss the applications of a Wilson-Cowan-type system, modeling the dynamics of two interacting populations of excitatory and inhibitory neurons. Furthermore, the presence of random input current, reflecting factors together with Poisson jumps, increases firing activity in neuronal systems.

Place, publisher, year, edition, pages
John Wiley & Sons, 2023
Keywords
compound Poisson process, excitatory neurons, finite activity jumps, inhibitory neurons, population dynamics, reflecting boundary condition, Skorokhod equations, stochastic differential equations, well-posedness, Wilson-Cowan equations
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-93020 (URN)10.1002/mma.8975 (DOI)000905516000001 ()2-s2.0-85145277197 (Scopus ID)
Available from: 2023-01-23 Created: 2023-01-23 Last updated: 2023-04-17Bibliographically approved
Nika, G. & Muntean, A. (2023). Hypertemperature effects in heterogeneous media and thermal flux at small-length scales. Networks and Heterogeneous Media, 18(3), 1207-1225
Open this publication in new window or tab >>Hypertemperature effects in heterogeneous media and thermal flux at small-length scales
2023 (English)In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 18, no 3, p. 1207-1225Article in journal (Refereed) Published
Abstract [en]

We propose an enriched microscopic heat conduction model that can account for size effects in heterogeneous media. Benefiting from physically relevant scaling arguments, we improve the regularity of the corrector in the classical problem of periodic homogenization of linear elliptic equations in the three-dimensional setting and, while doing so, we clarify the intimate role that correctors play in measuring the difference between the heterogeneous solution (microscopic) and the homogenized solution (macroscopic). Moreover, if the data are of form f = div F with (Formula presented), then we recover the classical corrector convergence theorem. 

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2023
Keywords
correctors, scale-size thermal effects, generalized Fourier's law, microstructure
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-93953 (URN)10.3934/nhm.2023052 (DOI)001039377000012 ()2-s2.0-85158820491 (Scopus ID)
Funder
Knowledge Foundation, 2020-0152
Available from: 2023-03-16 Created: 2023-03-16 Last updated: 2023-08-24Bibliographically approved
Kumazaki, K., Aiki, T. & Muntean, A. (2023). Local existence of a solution to a free boundary problem describing migration into rubber with a breaking effect. Networks and Heterogeneous Media, 18(1), 80-108
Open this publication in new window or tab >>Local existence of a solution to a free boundary problem describing migration into rubber with a breaking effect
2023 (English)In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 18, no 1, p. 80-108Article in journal (Refereed) Published
Abstract [en]

We consider a one-dimensional free boundary problem describing the migration of diffusants into rubber. In our setting, the free boundary represents the position of the front delimitating the diffusant region. The growth rate of this region is described by an ordinary differential equation that includes the effect of breaking the growth of the diffusant region. In this specific context, the breaking mechanism is should be perceived as a non-dissipative way of describing eventual hyperelastic response to a too fast diffusion penetration. In recent works, we considered a similar class of free boundary problems modeling diffusants penetration in rubbers, but without attempting to deal with the possibility of breaking or accelerating the occurring free boundaries. For simplified settings, we were able to show the global existence and uniqueness as well as the large time behavior of the corresponding solutions to our formulations. Since here the breaking effect is contained in the free boundary condition, our previous results are not anymore applicable. The main mathematical obstacle in ensuring the existence of a solution is the non-monotonic structure of the free boundary. In this paper, we establish the existence and uniqueness of a weak solution to the free boundary problem with breaking effect and give explicitly the maximum value that the free boundary can reach. 

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2023
Keywords
migration into rubber, free boundary problem, nonlinear initial-boundary value problem for nonlinear parabolic equations, existence of solutions, Flux boundary condition
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-92496 (URN)10.3934/nhm.2023004 (DOI)000922644200004 ()2-s2.0-85140482035 (Scopus ID)
Available from: 2022-11-16 Created: 2022-11-16 Last updated: 2023-02-25Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-1160-0007

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