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• 1.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
A model for the heat transfer between steel edge and running base in alpine racing skis2006In: WSEAS transactions on heat and mass transfer.,ISSN 1790-5044, 2006, Vol. 1, no 3, p. 256-261p. 256-261Conference paper (Refereed)
• 2.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the convergence and determination of limits for some sequences of differential operators: Presented at The Ninth International Conference on Integral Methods in Science and Engineering, Niagara Falls, Ontario, Canada, July 23-27 20062006Conference paper (Other academic)
• 3.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
Some remarks on homogenization in perforated domains2008In: Integral Methods in Science and Engineering: Techniques and Applications, Boston: Birkhäuser Verlag, 2008, p. 89-97Chapter in book (Other academic)
• 4.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On a heat transfer problem related to alpine ski racing2006In: Proceedings of the WSEAS HEAT '06, FLUID '06 : Elounda, Agios Nikolaos, Crete Island, Greece, August 21 - 23, 2006 ; 4th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment, 4th IASME/WSEAS International Conference on Fluid Mechanics and Aerodynamics: CD-rom, Elounda, Greece: WSEAS press , 2006, , p. 301-304Conference paper (Refereed)
• 5.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On some convergemce results and their relation to the impact of impurities on effective heat conduction properties2006In: Proceedings / 5th MATHMOD Vienna : February 8 - 10, 2006, Vienna University of Technology, Austria, Wien, 2006, , p. 16-1-16-7Conference paper (Refereed)
• 6.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the determination of limits for some sequences of functions and differential operators2006In: Canadian Applied Mathematics Quarterly, ISSN 1073-1849, Vol. 14, no 3, p. 299-329Article in journal (Refereed)

This article deals with homogenization methods, namely two-scale convergence and Hconvergence, with the aim of comparing their efficiency in studying composite materials. Analytic examples are given to illustrate both methods. While compensated compactness allows one to determine the limit of a product of two weakly converging sequences under additional assumptions on the derivatives, two-scale convergence takes advantage of underlying oscillations of solution sequences and H-convergence is concerned with the operator behaviour. Special attention is paid to periodic homogenization as this case yields the most involved results. Numerical experiments are used to investigate open questions in H-convergence dealing with the possible relaxation of some convergence hypotheses. Partial results are established in this respect.

• 7.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On a convergence result for sequences of functions with multiple scales2006In: Proceedings of the 9th WSEAS international conference on applied mathematics, Istanbul. Turkey., Aten: WSEAS press , 2006Conference paper (Refereed)
• 8.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the characterization of effective properties in highly heterogeneous media2005In: IASME transactions / International ASsociation of Mechanical Engineers, ISSN 1790-031X, Vol. 2, p. 177-179Article in journal (Refereed)

We discuss methods related to homogenization theory and G-convergence for the computation of effective properties in heterogeneous materials. Especially we investigate a method to detect deviations from the arithmetic mean in heterogeneous materials that are not necessarily periodic.

• 9.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the characterization of G-limits by means of some generalized two-scale techniques: Paper presented at the 26th Midwest-Pacific Differential Equations Conference, October 15-17, 2005, University of Alberta Edmonton, Alberta, Canada2005Conference paper (Refereed)

G-convergence usually deals with the convergence of sequences of elliptic or parabolic operators. When the convergence of the sequence of operators is strong enough, it is trivial to determine the $G$-limit. Other cases need sophisticated techniques for this aim, where the most well investigated case is periodic homogenization. The main tool of today for this purpose has become the so called two-scale convergence method by Nguetseng. This approach relies on a fundamental compactness result which says that for any bounded sequence $\left\{ u_{h}\right\}$ in $L^{2}\left( \Omega \right)$ there is $u_{0}\in L^{2}\left( \Omega \times Y\right)$ such that \begin{equation*} \dint\nolimits_{\Omega }u_{h}(x)\tau _{h}v(x)dx\rightarrow \dint\nolimits_{\Omega} \dint\nolimits_{Y}u_{0}(x,y)v(x,y)dxdy\end{equation*}% for any $v\in X=L^{2}(\Omega ;C_{\sharp }(Y))$ up to a subsequence, where% \begin{equation*} \tau _{h}v(x)=v(x,\frac{x}{\varepsilon _{h}}),\varepsilon _{h}\rightarrow 0% \text{.}\end{equation*} For gradients of sequences $\left\{ u_{h}\right\}$ bounded in $H^{1}\left( \Omega \right)$ the deviation from the week limit can be made explicit in terms of a local gradient $\nabla _{y}u_{1}$, $u_{1}\in L^{2}(\Omega;H_{\sharp }^{1}(Y))$, and this is the key to the characterization of the $G$%-limit. Similar techniques can be developed for other choices of the maps $\tau _{h}$ and admissible spaces $X$ which do not necessarily depend on any periodicity assumptions. We study such examples with respect to the possible appearance of residual terms corresponding to $\nabla _{y}u_{1}$ in periodic homogenization. In particular $G$-limits for problems, where the matrices defining the operators are generated by a kind of modified Hilbert-Schmidt operators, are investigated with respect to such deviations.

• 10.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the convergence of some pairs of weakly convergent sequences: Presented at the Applmath05 Fourth conference on applied mathematics and scientific computing June 19-24 Brijuni Island, Croatia2005Conference paper (Other academic)
• 11.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the convergence of some sequences of oscillating functionals2006In: WSEAS transactions on mathematics, ISSN 1109-2769, Vol. 5, no 8, p. 951-956Article in journal (Refereed)

We study an intermediate case between the two-scale convergence of Nguetseng and the more general concept of scale convergence of Mascarenhas and Toader. Suitable assumptions to provide scale convergence with some of the most essential properties of two-scale convergence are identified. Some aspects of the characterization of limits for sequences of gradients are discussed briefly.

• 12.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the characterization of effective properties in highly heterogeneous media (Proc.)2005In: Proceedings of the WSEAS HEAT '06, FLUID '06 : Elounda, Agios Nikolaos, Crete Island, Greece, August 21 - 23, 2006 ; 4th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment, 4th IASME/WSEAS International Conference on Fluid Mechanics and Aerodynamics Elounda, Greece, 2006, Elounda, Greece,, 2005, , p. -Conference paper (Refereed)

We discuss methods related to homogenization theory and G-convergence for the computation of effective properties in heterogeneous materials. Especially we investigate a method to detect deviations from the arithmetic mean in heterogeneous materials that are not necessarily periodic.

• 13.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On the relationship between some weak compactnesses with different numbers of scales2003Report (Other academic)

A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of non-periodic bounded functions in L²(). Further the relation to the classical notion of compensated compactness and the recent concept of two-scale compensated compactness is discussed and a defect measure for two-scale convergence is introduced.

• 14.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On two-scale convergence and related sequential compactness topics2006In: Applications of Mathematics, ISSN 0862-7940, Vol. 51, no 3, p. 247-262Article in journal (Refereed)

A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L 2(Ω) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced

• 15.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
G-convergence and Homogenization Involving Operators Compatible with Two-scale convergence2007Doctoral thesis, monograph (Other academic)
• 16.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
On general two-scale convergence and its application to the characterization of G-limits2007In: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 52, no 4, p. 285-302Article in journal (Refereed)

We characterize some G-limits using two-scale techniques and investigate a method to detect deviations from the arithmetic mean in the obtained G-limit, where no peirodicity assumptions are involved. We also prove some results on the properties of generalized two-scale convergence.

• 17.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Sequential convergence for functions and operators2004Licentiate thesis, monograph (Other academic)

The mathematical discipline homogenization theory is closely related to convergence issues. In this thesis different types of convergence are studied and put in relation to each other. We consider the classical concepts of G- and H-convergence and compensated compactness. The main focus, however, is on two-scale convergence which was originally adjusted to periodic homogenization but was later generalized to non-periodic cases. We point out some properties of the general version, where we use sequences of linear operators to obtain a two-scale limit, and identify conditions that make these operators compatible with two-scale convergence. A particular type of G-convergence is investigated using a specific choice of these two-scale compatible operators. Some considerations on how to introduce a defect measure for general two-scale convergence are put forward. The relationship between general two-scale convergence and the recent concept of unfolding is also studied. Finally, we illustrate H-convergence by means of periodic homogenization.

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