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Muntean, Adrianorcid.org/0000-0002-1160-0007

Open this publication in new window or tab >>Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data### Raveendran, Vishnu

### de Bonis, Ida

### Cirillo, Emilio N. M.

### Muntean, Adrian

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_some",{id:"formSmash:j_idt204:0:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_otherAuthors",{id:"formSmash:j_idt204:0:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_otherAuthors",multiple:true}); 2024 (English)In: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### 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)
#####

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##### Funder

Swedish Research Council, 2018-03648
Available from: 2024-01-14 Created: 2024-01-14 Last updated: 2024-02-27Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).

Sapienza Università di Roma, Italy.

Sapienza Università di Roma, Italy.

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).

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.

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### Lyons, Rainey

### Cirillo, Emilio N. M.

### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); 2024 (English)In: Nonlinear Analysis: Real World Applications, ISSN 1468-1218, Vol. 77, article id 104039Article in journal (Refereed) Published
##### Abstract [en]

##### 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)
#####

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##### Funder

Carl Tryggers foundation , CTS 21–1656
Available from: 2023-11-12 Created: 2023-11-12 Last updated: 2024-01-03Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).

Sapienza University of Rome, Italy.

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

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### Lyons, Rainey

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).### Muntean, Stela Andrea

### Cirillo, Emilio N.M.

### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); 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]

##### 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)
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##### 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

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).

University of Rome, Italy.

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.

Open this publication in new window or tab >>A mesoscopic lattice model for morphology formation in ternary mixtures with evaporation### Setta, Mario

### Kronberg, Vì C.E.

### Muntean, Stela Andrea

### Moons, Ellen

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); ### van Stam, Jan

### Cirillo, Emilio N.M.

### Colangeli, Matteo

### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_3_j_idt208_j_idt222",{id:"formSmash:j_idt204:3:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"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]

##### 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)
#####

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##### 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

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Università degli Studi dell’Aquila, Italy.

indhoven University of Technology, The Netherlands.

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).

Sapienza Università di Roma, Italy.

Università degli Studi dell’Aquila, Italy.

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.

Open this publication in new window or tab >>Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants### Nepal, Surendra

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).### Wondmagegne, Yosief

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_some",{id:"formSmash:j_idt204:4:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_otherAuthors",{id:"formSmash:j_idt204:4:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_otherAuthors",multiple:true}); 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]

##### 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)
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##### Funder

Swedish Research Council, 018-03648Knowledge Foundation, 019-021
Available from: 2022-11-20 Created: 2022-11-20 Last updated: 2023-02-25Bibliographically approved

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.

Open this publication in new window or tab >>Coupled stochastic systems of Skorokhod type: Well-posedness of a mathematical model and its applications### Thieu, Thi Kim Thoa

### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).### Melnik, Roderick

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_some",{id:"formSmash:j_idt204:5:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_otherAuthors",{id:"formSmash:j_idt204:5:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_otherAuthors",multiple:true}); 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]

##### 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)
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Available from: 2023-01-23 Created: 2023-01-23 Last updated: 2023-04-17Bibliographically approved

Wilfrid Laurier University, Canada.

Wilfrid Laurier University, Canada; BCAM—Basque Center for Applied Mathematics, Spain.

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.

Open this publication in new window or tab >>Hypertemperature effects in heterogeneous media and thermal flux at small-length scales### Nika, Grigor

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_some",{id:"formSmash:j_idt204:6:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_otherAuthors",{id:"formSmash:j_idt204:6:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_otherAuthors",multiple:true}); 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]

##### 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)
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##### Funder

Knowledge Foundation, 2020-0152
Available from: 2023-03-16 Created: 2023-03-16 Last updated: 2023-08-24Bibliographically approved

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.

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### Kumazaki, Kota

### Aiki, Toyohiko

### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_some",{id:"formSmash:j_idt204:7:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_otherAuthors",{id:"formSmash:j_idt204:7:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_otherAuthors",multiple:true}); 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]

##### 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)
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Available from: 2022-11-16 Created: 2022-11-16 Last updated: 2023-02-25Bibliographically approved

Nagasaki University, JPN.

Japan Women's University, JPN.

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.

Open this publication in new window or tab >>Model reduction of Brownian oscillators: Quantiﬁcation of errors and long-time behaviour### Colangeli, Matteo

### Duong, Manh Hong

### Muntean, Adrian

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_some",{id:"formSmash:j_idt204:8:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_otherAuthors",{id:"formSmash:j_idt204:8:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 56, article id 345003Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Institute of Physics (IOP), 2023
##### Keywords

model reduction, Wasserstein distance, error estimates, coupled Brownian oscillators, invariant manifold, Fluctuation–Dissipation relation
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:kau:diva-96133 (URN)10.1088/1751-8121/ace948 (DOI)001040008500001 ()2-s2.0-85167882122 (Scopus ID)
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Available from: 2023-07-20 Created: 2023-07-20 Last updated: 2023-08-29Bibliographically approved

University of L'Aquila, Italy.

University of Birmingham, United Kingdom.

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Arts and Social Sciences (starting 2013), Center for Societal Risk Research, CSR (from 2020).

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 Fluctuation–Dissipation relation. A general question thus arises as to whether one can rigorously quantify the error entailed by the use of the reduced dynamics in place of the original one. In this work we provide explicit formulae and estimates of the error in terms of the Wasserstein distance, both in the presence or in the absence of a sharp time-scale separation between the variables to be retained or eliminated from the description, as well as in the long-time behavior.

Open this publication in new window or tab >>Multiscale Carbonation Reactions: Status of Things and Two Modeling Exercises Related to Cultural Heritage### Muntean, Adrian

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_some",{id:"formSmash:j_idt204:9:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_otherAuthors",{id:"formSmash:j_idt204:9:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Mathematical Modeling in Cultural Heritage: MACH2021 / [ed] Gabriella Bretti; Cecilia Cavaterra; Margherita Solci; Michela Spagnuolo, Springer, 2023, p. 175-185Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2023
##### Series

Springer INdAM Series (SINDAMS), ISSN 2281-518X, E-ISSN 2281-5198 ; 55
##### Keywords

Carbonation reaction, Microstructure Porous media, Mathematical modelling, Multiscale reaction-diffusion problems, Cultural heritage
##### National Category

Mathematics Materials Chemistry
##### Research subject

Mathematics; Chemical Engineering
##### Identifiers

urn:nbn:se:kau:diva-96288 (URN)10.1007/978-981-99-3679-3_11 (DOI)2-s2.0-85169074629 (Scopus ID)978-981-99-3678-6 (ISBN)978-981-99-3681-6 (ISBN)978-981-99-3679-3 (ISBN)
##### Conference

INdAM Workshop: Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage–MACH2021, Rome, Italy, 13-15 September, 2021.
#####

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##### Funder

Swedish Research Council, 2018-03648
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2023-09-11Bibliographically approved

Having in mind as target audience beginner researchers working in the field of cultural heritage, we present succinctly the concept of two-scale modeling of reaction-diffusion problems as it fits to scenarios where the action of the carbonation reaction is relevant. We briefly review well-known contributions concerning multiscale concrete carbonation processes, and finally, we point out two related multiscale modeling exercises. The scope of these notes is twofold: Promoting the language of multiscale modeling, we invite the applied mathematician to pick some of the target problems from the context of cultural heritage. On the other hand, we invite the experimentalist to talk to the applied mathematician whenever the laboratory experiments are unable to answer questions for instance about the long time behavior of materials exposed to the ingress of various chemical species, humidity, and/or temperature (as it is the case of historical monuments and buildings in urban areas) because modeling and simulation approaches might provide at least provisory hints on what could happen further once measurements stop, or when the situation of interest takes place actually outside the laboratory.