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Träfflista för sökning "AMNE:(NATURVETENSKAP Matematik Matematisk analys) ;pers:(Muntean Adrian 1974)"

Sökning: AMNE:(NATURVETENSKAP Matematik Matematisk analys) > Muntean Adrian 1974

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1.
  • Raveendran, Vishnu (författare)
  • Homogenization of reaction-diffusion problems with nonlinear drift in thin structures
  • 2022
  • Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • We study the question of periodic homogenization of a variably scaled reaction-diffusion equation with non-linear drift of polynomial type. The non-linear drift was derived as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) for a population of interacting particles crossing a domain with obstacle. We consider three different geometries: (i) Bounded domain crossed by a finitely thin flat composite layer; (ii) Bounded domain crossed by an infinitely thin flat composite layer; (iii) Unbounded composite domain.\end{itemize} For the thin layer cases, we consider our reaction-diffusion problem endowed with slow or moderate drift. Using energy-type estimates as well as concepts like thin-layer convergence and two-scale convergence, we derive homogenized evolution equations and the corresponding effective model parameters. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interfaces. As a special scaling, the problem with large drift is treated separately for an unbounded composite domain. Because of the imposed large drift, this nonlinearity is expected to explode in the limit of a vanishing scaling parameter. To deal with this special case, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder's fixed point Theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in the unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials which are resistant to slow, moderate, and high velocity impacts. 
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  • Bourne, D., et al. (författare)
  • Is adding charcoal to soil a good method for CO2 sequestration? - : Modeling a spatially homogeneous soil
  • 2014
  • Ingår i: Applied Mathematical Modelling. - : Elsevier. - 0307-904X .- 1872-8480. ; 38:9-10, s. 2463-2475
  • Tidskriftsartikel (refereegranskat)abstract
    • Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools.We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g., type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2. © 2013 Elsevier Inc.
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  • Eden, Michael, 1987-, et al. (författare)
  • A multiscale quasilinear system for colloids deposition in porous media : Weak solvability and numerical simulation of a near-clogging scenario
  • 2022
  • Ingår i: Nonlinear Analysis. - : Elsevier. - 1468-1218. ; 63
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the weak solvability of a macroscopic, quasilinear reaction–diffusion system posed in a 2D porous medium which undergoes microstructural problems. The solid matrix of this porous medium is assumed to be made out of circles of not-necessarily uniform radius. The growth or shrinkage of these circles, which are governed by an ODE, has direct feedback to the macroscopic diffusivity via an additional elliptic cell problem. The reaction–diffusion system describes the macroscopic diffusion, aggregation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of this two-scale problem relies on a suitable application of Schauder's fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.
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  • Ijioma, Ekeoma Rowland, et al. (författare)
  • Pattern formation in reverse smouldering combustion : A homogenisation approach
  • 2013
  • Ingår i: Combustion theory and modelling. - : Taylor & Francis. - 1364-7830 .- 1741-3559. ; 17:2, s. 185-223
  • Tidskriftsartikel (refereegranskat)abstract
    • The development of fingering char patterns on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and through the use of phenomenological models. However, not much attention has been given to the behaviour of the emerging patterns based on characteristic material properties. Starting from a microscopic description of the combustion process, macroscopic models of reverse combustion that are derived by the application of the homogenisation technique are presented. Using proper scaling by means of a small scale parameter E, the results of the formal asymptotic procedure are justified by qualitative multiscale numerical simulations at the microscopic and macroscopic levels. We consider two equilibrium models that are based on effective conductivity contrasts, in a simple adiabatic situation, to investigate the formation of unstable fingering patterns on the surface of a charred material. The behaviour of the emerging patterns is analysed using primarily the Peclet and Lewis numbers as control parameters.
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  • Muntean, Adrian, 1974-, et al. (författare)
  • Homogenization Method and Multiscale Modeling
  • 2011
  • Bok (övrigt vetenskapligt/konstnärligt)abstract
    • This mini-course addresses graduate students and young researchers in mathematics and engineering sciences interested in applying both formal and rigorous averaging methods to real-life problems described by means of partial differential equations (PDEs) posed in heterogeneous media. As a background application scenario we choose to look at the interplay between reaction, diffusion and flow in periodic porous materials, but broadly speaking, a similar procedure would apply for, e.g., acoustic and/or electromagnetic wave propagation phenomena in composite (periodic) media as well. We start off with the study of oscillatory elliptic PDEs formulated firstly in fixed and, afterwards, in periodically-perforated domains. We remove the oscillations by means of a (formal) asymptotic homogenization method. The output of this procedure consists of a “guessed” averaged model equations and explicit rules (based on cell problems) for computing the effective coefficients. As second step, we introduce the concept of two-scale convergence (and correspondingly, the two-scale compactness) in the sense of Allaire and Nguetseng and derive rigorously the averaged PDE models and coefficients obtained previously. This step uses the framework of Sobolev and Bochner spaces and relies on basic tools like weak convergence methods, compact embeddings as well as extension theorems in Sobolev spaces. We particularly emphasize the role the choice of microstructures (pores, perforations, subgrids, etc.) plays in performing the overall averaging procedure. Finally, we focus our attention on a two-scale partly dissipative reaction-diffusion system with periodically distributed microstructure modeling chemical attack on concrete structures. We present a two-scale finite difference scheme able to approximate the unique weak solution to the two-scale system and prove its convergence. We illustrate numerically the typical micro-macro behavior of the active concentrations involved in the corrosion process and give details on how a two-scale FD scheme can be implemented in C. The main objective of the course is to endow the audience with a rather flexible mathematical homogenization tool so that he/she can quickly start applying this averaging methodology to other PDEs scenarios describing physico-chemical processes in media with microstructures.
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  • Ackelh, A.S., et al. (författare)
  • Preface to "modeling with measures"
  • 2015
  • Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences (AIMS). - 1547-1063 .- 1551-0018. ; 12:2
  • Tidskriftsartikel (refereegranskat)
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  • Aiki, Toyohiko, et al. (författare)
  • A free boundary problem describing migration into rubbers : Quest of the large time behavior
  • 2022
  • Ingår i: Zeitschrift für angewandte Mathematik und Mechanik. - : John Wiley & Sons. - 0044-2267 .- 1521-4001. ; 102:7
  • Tidskriftsartikel (refereegranskat)abstract
    • In many industrial applications, rubber-based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount of diffusants stored inside the material. In this framework, we prove the global solvability and explore the large time-behavior of solutions to a one-phase free boundary problem with nonlinear kinetic condition that is able to describe the migration of diffusants into rubber. The key idea in the proof of the large time behavior is to benefit from a contradiction argument, since it is difficult to obtain uniform estimates for the growth rate of the free boundary due to the use of a Robin boundary condition posed at the fixed boundary.
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  • Resultat 1-10 av 43

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