| 11. |
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| 12. |
- Holmbom, Anders, 1958-, et al.
(författare)
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A note on parabolic homogenization with a mismatch between the spatial scales
- 2013
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Ingår i: Abstract and Applied Analysis. - : Hindawi Publishing Corporation. - 1085-3375 .- 1687-0409. ; , s. Art. no. 329704-
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Tidskriftsartikel (refereegranskat)abstract
- We consider the homogenization of the linear parabolic problem rho(x/epsilon(2))partial derivative(t)u(epsilon)(x,t) - del . (a(x/epsilon(1), t/epsilon(2)(1))del u(epsilon) (x,t)) = f(x,t) which exhibits a mismatch between the spatial scales in the sense that the coefficient a(x/epsilon(1), t/epsilon(2)(1)) of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient rho(x/epsilon(2)) of the time derivative contains a faster spatial scale. It is shown that the faster spatialmicroscale does not give rise to any corrector termand that there is only one local problemneeded to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear.
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| 13. |
- Johnsen, Pernilla
(författare)
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Homogenization of Partial Differential Equations using Multiscale Convergence Methods
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of coefficient. We also consider a hyperbolic-parabolic problem with two spatial microscopic scales. The tools used are evolution settings of multiscale and very weak multiscale convergence, which are extensions of, or closely related to, the classical method of two-scale convergence. The novelty of the research in the thesis is the homogenization results and, for the studied parabolic problems, adapted compactness results of multiscale convergence type.
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| 14. |
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| 15. |
- Persson, Jens, 1978-
(författare)
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Homogenization of Some Selected Elliptic and Parabolic Problems Employing Suitable Generalized Modes of Two-Scale Convergence
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.
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| 16. |
- Persson, Jens, 1978-
(författare)
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Selected Topics in Homogenization
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The main focus of the present thesis is on the homogenization of some selected elliptic and parabolic problems. More precisely, we homogenize: non-periodic linear elliptic problems in two dimensions exhibiting a homothetic scaling property; two types of evolution-multiscale linear parabolic problems, one having two spatial and two temporal microscopic scales where the latter ones are given in terms of a two-parameter family, and one having two spatial and three temporal microscopic scales that are fixed power functions; and, finally, evolution-multiscale monotone parabolic problems with one spatial and an arbitrary number of temporal microscopic scales that are not restricted to be given in terms of power functions. In order to achieve homogenization results for these problems we study and enrich the theory of two-scale convergence and its kins. In particular the concept of very weak two-scale convergence and generalizations is developed, and we study an application of this convergence mode where it is employed to detect scales of heterogeneity.
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| 17. |
- Rineau, F., et al.
(författare)
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Carbon availability triggers the decomposition of plant litter and assimilation of nitrogen by an ectomycorrhizal fungus
- 2013
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Ingår i: The ISME Journal. - : nternational Society for Microbial Ecology. - 1751-7362 .- 1751-7370. ; 7:10, s. 2010-2022
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Tidskriftsartikel (refereegranskat)abstract
- The majority of nitrogen in forest soils is found in organic matter-protein complexes. Ectomycorrhizal fungi (EMF) are thought to have a key role in decomposing and mobilizing nitrogen from such complexes. However, little is known about the mechanisms governing these processes, how they are regulated by the carbon in the host plant and the availability of more easily available forms of nitrogen sources. Here we used spectroscopic analyses and transcriptome profiling to examine how the presence or absence of glucose and/or ammonium regulates decomposition of litter material and nitrogen mobilization by the ectomycorrhizal fungus Paxillus involutus. We found that the assimilation of nitrogen and the decomposition of the litter material are triggered by the addition of glucose. Glucose addition also resulted in upregulation of the expression of genes encoding enzymes involved in oxidative degradation of polysaccharides and polyphenols, peptidases, nitrogen transporters and enzymes in pathways of the nitrogen and carbon metabolism. In contrast, the addition of ammonium to organic matter had relatively minor effects on the expression of transcripts and the decomposition of litter material, occurring only when glucose was present. On the basis of spectroscopic analyses, three major types of chemical modifications of the litter material were observed, each correlated with the expression of specific sets of genes encoding extracellular enzymes. Our data suggest that the expression of the decomposition and nitrogen assimilation processes of EMF can be tightly regulated by the host carbon supply and that the availability of inorganic nitrogen as such has limited effects on saprotrophic activities.
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| 18. |
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| 19. |
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| 20. |
- Shah, Firoz, et al.
(författare)
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Secretion of iron(III)-reducing metabolites during protein acquisition by the ectomycorrhizal fungus paxillus involutus
- 2021
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Ingår i: Microorganisms. - : MDPI AG. - 2076-2607. ; 9:1
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Tidskriftsartikel (refereegranskat)abstract
- The ectomycorrhizal fungus Paxillus involutus decomposes proteins using a two-step mechanism, including oxidation and proteolysis. Oxidation involves the action of extracellular hydroxyl radicals (•OH) generated by the Fenton reaction. This reaction requires the presence of iron(II). Here, we monitored the speciation of extracellular iron and the secretion of iron(III)-reducing metabolites during the decomposition of proteins by P. involutus. X-ray absorption spectroscopy showed that extracellular iron was mainly present as solid iron(III) phosphates and oxides. Within 1 to 2 days, these compounds were reductively dissolved, and iron(II) complexes were formed, which remained in the medium throughout the incubation. HPLC and mass spectrometry detected five extracellular iron(III)-reducing metabolites. Four of them were also secreted when the fungus grew on a medium containing ammonium as the sole nitrogen source. NMR identified the unique iron(III)-reductant as the diarylcyclopentenone involutin. Involutin was produced from day 2, just before the elevated •OH production, preceding the oxidation of BSA. The other, not yet fully characterized iron(III)-reductants likely participate in the rapid reduction and dissolution of solid iron(III) complexes observed on day one. The production of these metabolites is induced by other environmental cues than for involutin, suggesting that they play a role beyond the Fenton chemistry associated with protein oxidation.
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