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  • 1. Berggren, Stein
    et al.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Meidell, Annette
    Wall, Peter
    Homogenization and computational techniques of iterated structures2001Ingår i: Proceedings of the Eight International Conference on Composites Engineering: ICCE/8 / [ed] David Hui, 2001Konferensbidrag (Refereegranskat)
  • 2.
    Brasch, Thomas von
    et al.
    Statistisk sentralbyrå og NUPI.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lystad, Lars Petter
    Narvik University College, 8505 Narvik, Norway.
    Fibonaccirekken i økonomifaget2013Ingår i: Samfunnsøkonomen, ISSN 1890-5250, Vol. 127, nr 2, s. 10-15Artikel i tidskrift (Refereegranskat)
  • 3.
    Brasch, Thomas von
    et al.
    Statistisk sentralbyrå.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lystad, Lars Petter
    Narvik University College, 8505 Narvik, Norway.
    Optimal control and the fibonacci sequence2012Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We bridge mathematical number theory with that of optimal control and show that a generalised Fibonacci sequence enters the control function of finite horizon dynamic optimisation problems with one state and one control variable. In particular, we show that the recursive expression describing the first-order approximation of the control function can be written in terms of a generalised Fibonacci sequence when restricting the final state to equal the steady state of the system. Further, by deriving the solution to this sequence, we are able to write the first-order approximation of optimal control explicitly. Our procedure is illustrated in an example often referred to as the Brock-Mirman economic growth model.

  • 4.
    Brasch, Thomas von
    et al.
    Research Department, Unit for Macroeconomics, Statistics Norway.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lystad, Lars Petter
    Department of Technology, Narvik University College.
    Optimal control and the Fibonacci sequence2012Ingår i: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 154, nr 3, s. 857-878Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We bridge mathematical number theory with optimal control and show that a generalised Fibonacci sequence enters the control function of finite-horizon dynamic optimisation problems with one state and one control variable. In particular, we show that the recursive expression describing the first-order approximation of the control function can be written in terms of a generalised Fibonacci sequence when restricting the final state to equal the steady-state of the system. Further, by deriving the solution to this sequence, we are able to write the first-order approximation of optimal control explicitly. Our procedure is illustrated in an example often referred to as the Brock-Mirman economic growth model

  • 5. Bylund, Nicklas
    et al.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Persson, Lars-Erik
    Reiterated homogenization with applications to autopart construction2001Ingår i: ICCE 8: Eight Annual International Conference on Composites Engineering / [ed] David Hui, 2001, s. 31-34Konferensbidrag (Refereegranskat)
  • 6.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Correctors for some nonlinear monotone operators2001Ingår i: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 8, nr 1, s. 8-30Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/εh,Duh)) = fh on Ω with Dirichlet boundary conditions. Here the sequence (εh) tends to 0 as h→∞ and the map a (x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions.W e prove that uh → u weakly in W1,p 0 (Ω) as h → ∞, where u is the solution of a homogenized problem of the form -div (b (x,Du)) = f on Ω. We also derive an explicit expression for the homogenized operator b and prove some corrector results, i.e. we find (Ph) such that Duh -Ph (Du) → 0 in Lp (Ω,Rn). () 0 in (Ω).

  • 7.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Correctors for some nonlinear monotone operators: Appendix with proofs1999Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Contains appendix with proofs to the publeshed article "J. Byström. Correctors for some nonlinear monotone operators. J. Nonlinear Math. Phys., ISSN: 1402-9251, 8:1 (2001), 8-30."

  • 8.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Influence of the inclusions distribution on the effective properties of heterogeneous media2003Rapport (Övrigt vetenskapligt)
  • 9.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Influence of the inclusions distribution on the effective properties of heterogeneous media2003Ingår i: Composites Part B: Engineering, ISSN 1359-8368, E-ISSN 1879-1069, Vol. 34, nr 7, s. 587-592Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we investigate the effective conductivity of composite materials by means of the homogenization method. We concentrate on composites with circular or elliptic cylindrical inclusions. In particular, we are interested in the effect of the distribution of the cylinders in the continuous material on the effective properties. We compare rectangular and hexagonal distributions with random distributions for different volume fractions of the inclusions. We also study the effect of the number of inclusions in each periodic cell for the random structure as well as shape influence of the elliptical inclusions.

  • 10.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Mathematical modelling of composites using the homogenization method2003Ingår i: Proceedings of the conference "MathTools-2003" / [ed] George Osipenko, 2003, s. 32-Konferensbidrag (Refereegranskat)
  • 11. Byström, Johan
    Optimal design of a long and slender compressive strut2009Ingår i: The International Journal of Multiphysics, ISSN 1750-9548, E-ISSN 2048-3961, Vol. 3, nr 3, s. 235-257Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This article deals with the optimal design of long and slender compressive struts. The main objective is to minimize the mass of the struts under certain non-failure constraints and thus find the optimal material. We show that the main failure mode of the struts is Euler buckling. The results clearly show that the struts should be constructed from unidirectional carbon fiber composites. A Monte-Carlo model for random microstructure homogenization of unidirectional composites is developed. We finish by performing a numerical computation of the effective properties of the chosen carbon fiber/epoxy composite using COMSOL MULTIPHYSICS software.

  • 12.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sharp constants for some inequalities connected to the p-Laplace operator2005Ingår i: Journal of Inequalities in Pure and Applied Mathematics, ISSN 1443-5756, E-ISSN 1443-5756, Vol. 6, nr 2, artikel-id 56Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we investigate a set of structure conditions used in the existence theory of differential equations. More specific, we find best constants for the corresponding inequalities in the special case when the differential operator is the p-Laplace operator.

  • 13.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some mathematical and engineering aspects of the homogenization theory2002Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis is devoted to some problems connected to the theory of homogenization of partial differential operators. The thesis consists of an elementary introduction and five different parts, A-E. In the introduction we give an elementary presentation of the basic ideas in the homogenization theory. Moreover, the introduction also serves as an overview of the field and points out where the results contained in this thesis fit in. The first part, Part A, consists of two papers with a complementary appendix and deals some purely theoretical parts of homogenization theory. Part B consists of one paper dealing with bounds of the homogenized operator. The third part, Part C, consists of two papers concerning some computational aspects of homogenization. Part D consists of two papers which show how the theoretical results from the homogenization theory can be practically used in composites engineering. Finally, Part E consists of two papers presented at international conferences, which consider some further mathematical and engineering aspects of the homogenization method.

  • 14.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new developments and applications of the homogenization theory1999Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis is devoted to some problems connected to the theory of homogenization of partial differential operators. The thesis consists of an introduction and three different parts, A-C. In the introduction we give an elementary presentation of the basic ideas in the homogenization theory. Moreover, the introduction also serves as an overview of the field and points out where the results contained in this thesis fit in. The first part, Part A, consists of one paper with a complementary appendix and deals with the limit behavior of the solutions of a sequence of quasi-linear equations. Part B consists of one paper with a complementary appendix in which the homogenization theory is used for the evaluation of different semi-analytical models used in the determination of the elastic properties of woven composites. The third part, Part C, consists of three papers which consider some further mathematical and engineering aspects of the homogenization method. Several numerical and experimental results are also presented and compared with theoretical results.

  • 15.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Dasht, Johan
    Wall, Peter
    A numerical study of stochastic homogenization2003Ingår i: Proceedings of the International Conference on Composites Engineering: ICCE/10 / [ed] David Hui, 2003Konferensbidrag (Refereegranskat)
  • 16. Byström, Johan
    et al.
    Dasht, Johan
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    A numerical study of the convergence in stochastic homogenization2004Ingår i: Journal of Analysis and Applications, ISSN 0972-5954, Vol. 2, nr 3, s. 159-171Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This note makes the link between theoretical results on stochastic homogenization and effective computation of averaged coefficients for diffusion operators in random media. Examples of how to construct relevant random media and numerical results on the effective coefficients are given.

  • 17. Byström, Johan
    et al.
    Engström, Jonas
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Bounds and numerical results for the homogenized degenerated p-Poisson equation2004Ingår i: Applications of Mathematics, ISSN 0862-7940, E-ISSN 1572-9109, Vol. 49, nr 2, s. 111-122Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we derive upper and lower bounds on the homogenized energy density functional corresponding to degenerated p-Poisson equations. Moreover, we give some non-trivial examples where the bounds are tight and thus can be used as good approximations of the homogenized properties. We even present some cases where the bounds coincide and also compare them with some numerical results.

  • 18.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Engström, Jonas
    Wall, Peter
    Periodic approximation of elastic properties in random media2006Ingår i: Advances in Algebra and Analysis, ISSN 0973-2306, Vol. 1, nr 2, s. 103-113Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Most papers on stochastic homogenization either deal with theoretical aspects or with questions regarding computational issues. Since the theoretical analysis involves the solution of a problem which is stated in a abstract probability space, it is not clear how the two areas are connected. In previous works this problem has not been considered. However, recently Bourgeat and Piatnitski investigated this connection in the scalar case for second order operators of divergence form. They proved that in the limit, the method of periodic approximation gives the same effective properties as in stochastic homogenization. In this paper we prove similar results for the vector valued case, which appears in e.g. the theory of elasticity. Moreover, we provide a numerical analysis of the results.

  • 19.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Engström, Jonas
    Wall, Peter
    Reiterated homogenization of degenerate nonlinear elliptic equations2002Ingår i: Chinese Annals of Mathematics. Series B, ISSN 0252-9599, E-ISSN 1860-6261, Vol. 23, nr 3, s. 325-334Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The authors study homogenization of some nonlinear partial differential equations of the form _ div (a (hx, h2 x, Duh)) = f , where a is periodic in the rst two arguments and monotone in the third. In particular the case where a satis es degenerated structure conditions is studied. It is proved that uh converges weakly in W0 1,1 (Ω) to the unique solution of a limit problem as h → ∞ . Moreover, explicit expressions for the limit problem are obtained.

  • 20. Byström, Johan
    et al.
    Engström, Jonas
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Reiterated homogenization of degenerate nonlinear monotone operators2004Ingår i: Frontiers in Mathematical Analysis and Numerical Methods: In Memory of Jacques-Louis Lions, Singapore: World Scientific and Engineering Academy and Society, 2004, s. 83-96Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 21.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Helsing, Johan
    Kungliga tekniska högskolan, KTH.
    Meidell, Annette
    Narvik University College, 8505 Narvik, Norway.
    Some computational aspects of iterated structures2001Ingår i: Composites Part B: Engineering, ISSN 1359-8368, E-ISSN 1879-1069, Vol. 32, nr 6, s. 485-490Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider some computational aspects of effective properties for some multi-scale structures. In particular, we discuss iterated square honeycombs and another type of square honeycombs containing up to 4000 small discs randomly distributed inside each square. We present some numerical methods for estimating the effective conductivity with good control of the accuracy.

  • 22.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Jekabsons, Normunds
    Persson, Lars-Erik
    A comparison of different homogenization models and experimental results1999Ingår i: ICCE 6: Sixth Annual International Conference on Composites Engineering / [ed] David Hui, 1999, s. 97-98Konferensbidrag (Refereegranskat)
  • 23.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Jekabsons, Normunds
    Luleå tekniska universitet.
    Varna, Janis
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    An evaluation of different models for prediction of elastic properties of woven composites2000Ingår i: Composites Part B: Engineering, ISSN 1359-8368, E-ISSN 1879-1069, Vol. 31, nr 1, s. 7-20Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A critical analysis of two simple and convenient analytical models for calculation of elastic properties of woven fabric composites is performed. Predictions of these models are compared with results obtained using the method of reiterated homogenization and with experimental data for plain weave glass fiber and carbon fiber polyester composites. Three different scales are identified in the analysis. The first scale predictions, which are the tow properties (obtained by applying Hashin's concentric cylinder model, the Halpin-Tsai expressions or mathematical homogenization technique), are the most critical because they form the input information for woven composite modeling. It appears that the uncertainty in this information causes larger differences in predictions than the deviations between models of different degree of accuracy. This fact sets limits on the required accuracy of the models. Model comparisons reveal that the woven compoiste model based on isostrain assumption in the compoiste plane and isostress assumption for out-of-plane components is in very good agreement with both experimental data and the reiterated homogenization method, whereas the modified mosaic parallel model fails to describe composites with large interlaced regions.

  • 24.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Kuzmin, Leonid
    Cross section dependence on ski pole stiffness2013Rapport (Refereegranskat)
    Abstract [en]

    Ski equipment producer SWIX has recently presented a new pair of ski poles,called SWIX Triac, which di¤ers from conventional (round) ski poles by having atriangular cross section. SWIX claims that the main objective for this design is thatit has superior sti¤ness to weight ratio compared to common ski poles. We provein this paper that this claim in general is not true. More speci…c, we show thatfor thin walled cross sections, a hollow circular cross section has up to 36% bettersti¤ness to weight ratio than a corresponding triangular cross section.

  • 25.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lystad, Lars Petter
    Department of Technology, Narvik University College.
    Nyman, Per-Ole
    Department of Technology, Narvik University College.
    Using generalized Fibonacci sequences for solving the one-dimensional LQR problem and its discrete-time Riccati equation2010Ingår i: Modeling, Identification and Control, ISSN 0332-7353, E-ISSN 1890-1328, Vol. 31, nr 1, s. 1-18Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article we develop a method of solving general one-dimensional Linear Quadratic Regulator (LQR) problems in optimal control theory, using a generalized form of Fibonacci numbers. We find the solution R (k) of the corresponding discrete-time Riccati equation in terms of ratios of generalized Fibonacci numbers. An explicit Binet type formula for R (k) is also found, removing the need for recursively finding the solution at a given timestep. Moreover, we show that it is also possible to express the feedback gain, the penalty functional and the controller state in terms of these ratios. A generalized golden ratio appears in the corresponding in finite horizon problem. Finally, we show the use of the method in a few examples.

  • 26.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Persson, Lars-Erik
    Random versus periodic cells in homogenization2002Ingår i: ICCE 9: Ninth Annual International Conference on Composites Engineering / [ed] David Hui, 2002, s. 83-84Konferensbidrag (Refereegranskat)
  • 27.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Persson, Lars-Erik
    Tillämpad matematik: en populär introduktion för lärare och ingenjörer2004Ingår i: Kvinnor och matematik : konferens den 12-14 april 2002: konferensrapport / [ed] Barbro Grevholm; Lisbeth Lindberg, Kristianstad: Högskolan Kristianstad , 2004, s. 37-48Konferensbidrag (Övrigt vetenskapligt)
  • 28.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Persson, Lars-Erik
    Jekabsons, Normunds
    Luleå tekniska universitet.
    Varna, Janis
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    Using reiterated homogenization for stiffness computation of woven composites1998Ingår i: ICCE 5: Fifth International Conference on Composites Engineering / [ed] David Hui, 1998, s. 133-134Konferensbidrag (Refereegranskat)
  • 29.
    Byström, Johan
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Heat conductivity bounds by Halpin-Tsai type equations and homogenization2000Ingår i: Proceedings of the Seventh International Conference on Composites Engineering: ICCE/7 / [ed] David Hui, 2000, s. 97-98Konferensbidrag (Refereegranskat)
  • 30.
    Homola, Matthew
    et al.
    Narvik University College, 8505 Narvik, Norway.
    Byström, Johan
    Nicklasson, Per Johan
    Narvik University College, 8505 Narvik, Norway.
    Sundsbø, Per Arne
    Narvik University College, 8505 Narvik, Norway.
    A corrector for wind power estimation and its usage in estimating icing losses2008Konferensbidrag (Övrigt vetenskapligt)
  • 31.
    Jekabsons, Normunds
    et al.
    Luleå tekniska universitet.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On the effect of stacked fabric layers on the stiffness of a woven composite2002Ingår i: Composites Part B: Engineering, ISSN 1359-8368, E-ISSN 1879-1069, Vol. 33, nr 8, s. 619-629Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Most micromechanical models for stiffness prediction of woven composites assume independence of the Q-matrix on the number of fabric layers in the composite. For example, the moduli of single and 10 layer composites are assumed to be equal in the case when all layers have the same in-plane orientation. Although this statement is likely to be true for isotropic materials or even for unidirectional laminated composites, it may not be valid in some cases of woven composites. This paper contains experimental and theoretical investigations of plain weave carbon fiber/polyester composites. Specimens with one single and eight layers of fabrics are tested and observable differences of mechanical properties are obtained. The theoretical part of this article consists of derivation and application of several micromechanical models on these particular composites. The use of those simplified models finally allows us to find the main mechanisms which cause the observed effects.

  • 32. Lukkassen, Dag
    et al.
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Pavval, Anneli
    Luleå tekniska universitet.
    Persson, Lars-Erik
    Computing effective conductivities by bounds and numerical methods1997Ingår i: ICCE 4: Fourth International Conference on Composites Engineering / [ed] David Hui, 1997, s. 199-200Konferensbidrag (Refereegranskat)
  • 33.
    Maad, Sara
    et al.
    University of Virginia.
    Martin, Clyde
    Texas Tech University.
    Strömberg, Thomas
    Byström, Johan
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Surface fitting with boundary data2004Ingår i: 2004 43rd IEEE Conference on Decision and Control: Nassau, Bahamas, 14 - 17 December 2004, Piscataway, NJ: IEEE Communications Society, 2004, Vol. Vol. 4, s. 3649-3653Konferensbidrag (Refereegranskat)
    Abstract [en]

    The problem of fitting surfaces to data is a well studied problem in statistics. However when there is prior information the theory is not developed. It often happens in toxicology and in medicine that the effect of a single drug is well understood.. However if a pair of drugs is delivered in tandem or if two toxins are interacting the effect is not understood. In this paper we attack the problem of fitting a surface to a data set contained in a square when two of the boundaries are known. Our approach generalizes the concept of smoothing splines.

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