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  • 1.
    Adamowicz, Tomasz
    et al.
    Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures2016In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, no 2, p. 623-658Article in journal (Refereed)
    Abstract [en]

    We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-domains), we show the boundary Harnack inequality for p(⋅)-harmonic functions under the assumption that the variable exponent p is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson-type estimate for p(⋅)-harmonic functions in NTA domains in Rn and provide lower and upper growth estimates and a doubling property for a p(⋅)-harmonic measure.

  • 2. Aidanpää, Jan - Olov
    et al.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Developments in rotor dynamical modeling of hydropower units2009Conference paper (Refereed)
  • 3.
    Avelin, Benny
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Boundary estimates for solutions to operators of p-Laplace type with lower order terms2011In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 250, no 1, p. 264-291Article in journal (Refereed)
    Abstract [en]

    In this paper we study the boundary behavior of solutions to equations of the form∇⋅A(x,∇u)+B(x,∇u)=0, in a domain ΩRn, assuming that Ω is a δ-Reifenberg flat domain for δ sufficiently small. The function A is assumed to be of p-Laplace character. Concerning B, we assume that |∇ηB(x,η)|⩽c|η|p−2, |B(x,η)|⩽c|η|p−1, for some constant c, and that B(x,η)=|η|p−1B(x,η/|η|), whenever xRn, ηRn∖{0}. In particular, we generalize the results proved in J. Lewis et al. (2008) [12] concerning the equation ∇⋅A(x,∇u)=0, to equations including lower order terms.

  • 4.
    Avelin, Benny
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Optimal doubling, reifenberg flatness and operators of p-laplace type2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 17, p. 5943-5955Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider equations of p-Laplace type of the form A(x,u)=0. Concerning A we assume, for p∈(1,) fixed, an appropriate ellipticity type condition, Hölder continuity in x and that A(x,η)=|η|p−1A(x,η/|η|) whenever xRn and ηRn∖{0}. Let ΩRn be a bounded domain, let D be a compact subset of Ω. We say that is the A-capacitary function for D in Ω if on D, on Ω in the sense of and in ΩD in the weak sense. We extend to RnΩ by putting on RnΩ. Then there exists a unique finite positive Borel measure on Rn, with support in Ω, such that In this paper, we prove that if Ω is Reifenberg flat with vanishing constant, then for every τ, 0<τ≤1. In particular, we prove that is an asymptotically optimal doubling measure on Ω.

  • 5.
    Grafström, Anton
    et al.
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Why well spread probability samples are balanced2013In: Open Journal of Statistics, ISSN 2161-718X, E-ISSN 2161-7198, Vol. 3, no 1, p. 36-41Article in journal (Refereed)
    Abstract [en]

    When sampling from a finite population there is often auxiliary information available on unit level. Such information can be used to improve the estimation of the target parameter. We show that probability samples that are well spread in the auxiliary space are balanced, or approximately balanced, on the auxiliary variables. A consequence of this balancing effect is that the Horvitz-Thompson estimator will be a very good estimator for any target variable that can be well approximated by a Lipschitz continuous function of the auxiliary variables. Hence we give a theoretical motivation for use of well spread probability samples. Our conclusions imply that well spread samples, combined with the HorvitzThompson estimator, is a good strategy in a varsity of situations.

  • 6.
    Grafström, Anton
    et al.
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Lundström, Niklas LP
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Schelin, Lina
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Spatially balanced sampling through the pivotal method2012In: Biometrics, ISSN 0006-341X, E-ISSN 1541-0420, Vol. 68, no 2, p. 514-520Article in journal (Refereed)
    Abstract [en]

    A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

  • 7. Lewis, John L.
    et al.
    Lundström, Niklas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Boundary Harnack inequalities for operators of p-Laplace type in Reifenberg flat domains2008In: Perspectives in Partial Differential Equations, Harmonic Analysis and Applications: A Volume in Honor of Vladimir G. Maz'ya's 70th Birthday / [ed] Dorina Mitrea and Marius Mitrea, American Mathematical Society (AMS), 2008, Vol. 79, p. 229-266Chapter in book (Refereed)
    Abstract [en]

    In this paper we highlight a set of techniques that recently have been used to establish boundary Harnack inequalities for p-harmonic functions vanishing on a portion of the boundary of a domain which is ‘flat’ in the sense that its boundary is well-approximated by hyperplanes. Moreover, we use these techniques to establish new results concerning boundary Harnack inequalities and the Martin boundary problem for operators of p-Laplace type with variable coefficients in Reifenberg flat domains.

  • 8.
    Lindh, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Lund University.
    Bolmgren, Kjell
    SLU.
    Lundström, Niklas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Jonzén, Niclas
    Lund University.
    Constrained growth flips the direction of optimal phenological responses among annual plants2016In: New Phytologist, ISSN 0028-646X, E-ISSN 1469-8137, Vol. 209, no 4, p. 1591-1599Article in journal (Refereed)
    Abstract [en]

    Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.

  • 9.
    Lundström, Niklas
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Aidanpää, Jan - Olov
    Dynamic Consequences of Electromagnetic Pull Due to Deviations in Generator Shape2007In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 301, no 1-2, p. 207-225Article in journal (Refereed)
    Abstract [en]

    Results from earlier measurements on hydropower generators have indicated relatively large eccentricities and shape deviations in the rotor and stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The UMP force can produce large vibrations which can be dangerous to the machine. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained through the law of energy conservation. The target of the paper is to analyse the dynamics of a generator due to shape deviations in the rotor and stator. As rotor-model, a balanced Jeffcott rotor is used. A linearization of the UMP indicates the importance of considering the nonlinear effects. The stability of some attractors are analysed and the generator dynamics are further investigated by simulating the basin of attraction. The magnitudes are approximately obtained when the shape deviations become dangerous for the generator. It is concluded which shape deviations that are more dangerous than others. In hydropower generator maintenance the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and estimate the stability and robustness by simulations. (c) 2006 Elsevier Ltd. All rights reserved.

  • 10.
    Lundström, Niklas
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Aidanpää, Jan - Olov
    Whirling Frequencies and Amplitudes due to Deviations of Generator Shape2008In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 43, no 9, p. 933-940Article in journal (Refereed)
    Abstract [en]

    Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles. due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator. and the corresponding LIMP is obtained by using the law of energy conservation. The LIMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the LIMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling. can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.

  • 11.
    Lundström, Niklas L P
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Estimates for p-harmonic functions vanishing on a flat2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 18, p. 6852-6860Article in journal (Refereed)
    Abstract [en]

    We study p-harmonic functions in a domain ΩCRn near an m-dimensional plane (an m-flat) Λm, where 0≤mn−1. In particular, let u be a positive p-harmonic function, with n<p, vanishing on a portion of Λm, and suppose that β=(pn+m)/(p−1), with β=1 if p=. We prove, using certain barrier functions, that 

     u ≈ d (x.Λm)8   near Λm.

    The lower bound holds also in the range nm<p. Moreover, uC0,β near Λm and β is the optimal Hölder exponent of u.

  • 12.
    Lundström, Niklas L. P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    How to find simple nonlocal stability and resilience measures2018In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 93, no 2, p. 887-908Article in journal (Refereed)
    Abstract [en]

    Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local stability and resilience measures, based on linearizations, accounting only for arbitrary small perturbations. Using numerical estimates of the size and shape of the basin of attraction, as well as the systems returntime to the attractor after given a perturbation, we construct simple nonlocal stability and resilience measures that record a systems ability to tackle both large and small perturbations. We demonstrate our approach on the Solow-Swan model of economic growth, an electro-mechanical system, a stage-structured population model as well as on a high-dimensional system, and conclude that the suggested measures detect dynamic behavior, crucial for a systems stability and resilience, which can be completely missed by local measures. The presented measures are also easy to implement on a standard laptop computer. We believe that our approach will constitute an important step toward filling a current gap in the literature by putting forward and explaining simple ideas and methods, and by delivering explicit constructions of several promising nonlocal stability and resilience measures.

  • 13.
    Lundström, Niklas L P
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Phragmén-Lindelöf theorems and p-harmonic measures for sets near low-dimensional hyperplanes2016In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 44, no 2, p. 313-330Article in journal (Refereed)
    Abstract [en]

    We prove estimates of a p-harmonic measure, p∈(nm,], for sets in R n which are close to an m-dimensional hyperplane Λ⊂R n , m∈[0,n−1]. Using these estimates, we derive results of Phragmén-Lindelöf type in unbounded domains Ω⊂R n ∖Λ for p-subharmonic functions. Moreover, we give local and global growth estimates for p-harmonic functions, vanishing on sets in R n , which are close to an m-dimensional hyperplane.

  • 14.
    Lundström, Niklas L. P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Loeuille, Nicolas
    Meng, Xinzhu
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, China.
    Bodin, Mats
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Meeting yield and conservation objectives by harvesting both juveniles and adults2019In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 193, no 3, p. 373-390Article in journal (Refereed)
    Abstract [en]

    Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as "pretty good yields" (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured model and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, although our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g., basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and size structure, so that these later quantities can provide integrative signals to detect possible collapses.

  • 15.
    Lundström, Niklas L P
    et al.
    Department of Mathematics, Uppsala University, Sweden.
    Nyström, Kaj
    Department of Mathematics, Uppsala University, Sweden.
    Olofsson, Marcus
    Department of Mathematics, Uppsala University, Sweden.
    Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type2014In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 4, p. 1213-1247Article in journal (Refereed)
    Abstract [en]

    In this paper we study the system where . A special case of this type of system of variational inequalities with terminal data occurs in the context of optimal switching problems. We establish a general comparison principle for viscosity sub- and supersolutions to the system under mild regularity, growth, and structural assumptions on the data, i.e., on the operator and on continuous functions , , and . A key aspect is that we make no sign assumption on the switching costs and that is allowed to depend on as well as . Using the comparison principle, the existence of a unique viscosity solution to the system is constructed as the limit of an increasing sequence of solutions to associated obstacle problems. Having settled the existence and uniqueness, we subsequently focus on regularity of beyond continuity. In this context, in particular, we assume that belongs to a class of second-order differential operators of Kolmogorov type of the form: where . The matrix is assumed to be symmetric and uniformly positive definite in . In particular, uniform ellipticity is only assumed in the first coordinate directions, and hence, may be degenerate.

  • 16.
    Lundström, Niklas L. P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zhang, Hong
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Financial Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria.
    Pareto-efficient biological pest control enable high efficacy at small costs2017In: Ecological Modelling, ISSN 0304-3800, E-ISSN 1872-7026, Vol. 364, p. 89-97Article in journal (Refereed)
    Abstract [en]

    Biological pest control is increasingly used in agriculture as an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of naturally occurring and/or genetically modified enemies such as predators, parasitoids, or pathogens. As the interaction between these enemies and the pest is complex and the production of natural enemies potentially expensive, it is not surprising that both the efficacy and economic viability of biological pest control are debated. Here, we investigate the performance of very simple control strategies. In particular, we show how Pareto-efficient one-off or periodic release strategies, that optimally trade off between efficacy and economic viability, can be devised and used to enable high efficacy at small economic costs. We demonstrate our method on a pest–pathogen–crop model with a tunable immigration rate of pests. By analyzing this model, we demonstrate that simple Pareto-efficient one-off and periodic release strategies are efficacious and simultaneously have profits that are close to the theoretical maximum obtained by strategies optimizing only the profit. When the immigration rate of pests is low to intermediate, one-off control strategies are sufficient, and when the immigration of pests is high, periodic release strategies are preferable. The methods presented here can be extended to more complex scenarios and be used to identify promising biological pest control strategies in many circumstances.

  • 17. Lundström, Niklas L.P.
    Bifurcations and Strange Attractors in a Climate Related System2005In: Differentsial'nye Uravneniya i Protsessy Upravleniya / Differential Equations and Control Processes

    , ISSN 1817-2172, E-ISSN 1817-2172, no 1, p. 1-53
    Article in journal (Refereed)
    Abstract [en]

    R. V. Bekryaev derived a system for a horizontally baroclinic atmosphere consisting of six ordinary differential equations. We prove dissipativity and find estimates for the location of the global attractor. The evolution of a complicated attractor is analysed with a Poincar'e map showing difficult bifurcation behaviour. Investigations in bifurcation diagrams show a rich dynamical behaviour including a lot of known complicated bifurcations, of which a fold-Hopf bifurcation is examined in detail. Finally, we give some theory about the Lyapunov spectra and present a method for determining the exponents.

  • 18.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    p-harmonic functions near the boundary2011Doctoral thesis, comprehensive summary (Other academic)
  • 19.
    Lundström, Niklas L.P.
    et al.
    Division of Solid Mechanics, Luleå University of Technology, Luleå, SWEDEN.
    Aidanpää, Jan - Olov
    Division of Solid Mechanics, Luleå University of Technology, Luleå, SWEDEN.
    Complex dynamic responses due to deviations of generator shape2009In: 10th CONFERENCE on Dynamical Systems: Theory and Applications, 2009Conference paper (Refereed)
    Abstract [en]

    Earlier measurements in large synchronous generators indicate the existence of complex whirling motion, and also deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called Unbalanced Magnetic Pull (UMP). The target of this paper is to analyse responses due to certain deviations of shape in the rotor and the stator. In particular, the perturbation on the rotor is considered to be of oval character, and the perturbations of the stator are considered triangular and eccentric. It is concluded that harmful conditions can occur due to high amplitudes especially when the whirling of the rotor changes from forward to backward. During maintenance of hydro power generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complex whirling motion.

  • 20.
    Lundström, Niklas L.P.
    et al.
    Division of Solid Mechanics, Department of Applied Physics and Mechanical Engineering, Luleå University of Technology.
    Aidanpää, Jan - Olov
    Division of Solid Mechanics, Department of Applied Physics and Mechanical Engineering, Luleå University of Technology.
    Dynamics in large generators due to oval rotorand triangular stator shape2011In: Acta Mechanica Sinica, ISSN 0567-7718, E-ISSN 0459-1879, Vol. 27, no 1, p. 18-27Article in journal (Refereed)
    Abstract [en]

    Earlier measurements in large synchronous generatorsindicate the existence of complex whirling motion,and also deviations of shape in both the rotor and the stator.These non-symmetric geometries produce an attraction forcebetween the rotor and the stator, called unbalanced magneticpull (UMP). The target of this paper is to analyse responsesdue to certain deviations of shape in the rotor and the stator.In particular, the perturbation on the rotor is consideredto be of oval character, and the perturbations of the statorare considered triangular. By numerical and analytical methodsit is concluded for which generator parameters harmfulconditions, such as complicated whirling motion and highamplitudes, will occur. During maintenance of hydro powergenerators the shapes of the rotor and stator are frequentlymeasured. The results from this paper can be used to evaluatesuch measurements and to explain the existence of complexwhirling motion.

  • 21.
    Lundström, Niklas L.P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Applied Physics and Mechanical Engineering, Luleå University of Technology, SE-97187 Luleå, Sweden .
    Grafström, Anton
    Department of Forest Resource Management, Swedish University of Agricultural Sciences, SE-90337 Umeå, Sweden .
    Aidanpää, Jan-Olov
    Department of Applied Physics and Mechanical Engineering, Luleå University of Technology, SE-97187 Luleå, Sweden .
    Small shape deviations causes complex dynamics in large electric generators2014In: European Physical Journal: Applied physics, ISSN 1286-0042, E-ISSN 1286-0050, Vol. 66, no 2, p. 20903-Article in journal (Refereed)
    Abstract [en]

    We prove that combinations of small eccentricity, ovality and/or triangularity in the rotor and stator can produce complex whirling motions of an unbalanced rotor in large synchronous generators. It is concluded which structures of shape deviations that are more harmful, in the sense of producing complex whirling motions, than others. For each such structure, we derive simplified equations of motions from which we conclude analytically the relation between shape deviations and mass unbalance that yield non-smooth whirling motions. Finally we discuss validity of our results in the sense of modeling of the unbalanced magnetic pull force.

  • 22.
    Lundström, Niklas L.P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On a two-phase free boundary condition for p-harmonic measures2009In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 129, no 2, p. 231-249Article in journal (Refereed)
    Abstract [en]

    Let Ωi⊂Rn,i∈{1,2} , be two (δ, r 0)-Reifenberg flat domains, for some 0<δ<δ^ and r 0 > 0, assume Ω1∩Ω2=∅ and that, for some w∈Rn and some 0 < r, w∈∂Ω1∩∂Ω2,∂Ω1∩B(w,2r)=∂Ω2∩B(w,2r) . Let p, 1 < p < ∞, be given and let u i , i∈{1,2} , denote a non-negative p-harmonic function in Ω i , assume that u i , i∈{1,2}, is continuous in Ω¯i∩B(w,2r) and that u i = 0 on ∂Ωi∩B(w,2r) . Extend u i to B(w, 2r) by defining ui≡0 on B(w,2r)∖Ωi. Then there exists a unique finite positive Borel measure μ i , i∈{1,2} , on R n , with support in ∂Ωi∩B(w,2r) , such that if ϕ∈C∞0(B(w,2r)) , then∫Rn|∇ui|p−2⟨∇ui,∇ϕ⟩dx=−∫Rnϕdμi.Let Δ(w,2r)=∂Ω1∩B(w,2r)=∂Ω2∩B(w,2r) . The main result proved in this paper is the following. Assume that μ 2 is absolutely continuous with respect to μ 1 on Δ(w, 2r), d μ 2 = kd μ 1 for μ 1-almost every point in Δ(w, 2r) and that logk∈VMO(Δ(w,r),μ1) . Then there exists δ~=δ~(p,n)>0 , δ~<δ^ , such that if δ≤δ~ , then Δ(w, r/2) is Reifenberg flat with vanishing constant. Moreover, the special case p = 2, i.e., the linear case and the corresponding problem for harmonic measures, has previously been studied in Kenig and Toro (J Reine Angew Math 596:1–44, 2006).

  • 23.
    Lundström, Niklas L.P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The Boundary Harnack Inequality for Solutions to Equations of Aronsson type in the Plane2011In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 36, p. 261-278Article in journal (Refereed)
    Abstract [en]

    In this paper we prove a boundary Harnack inequality for positive functions which vanish continuously on a portion of the boundary of a bounded domain \Omega \subset R2 and which are solutions to a general equation of p-Laplace type, 1 < p < \infty. We also establish the same type of result for solutions to the Aronsson type equation \nabla (F(x,\nabla u)) \cdot F\eta(x,\nabla u) = 0. Concerning \Omega we only assume that \partial\Omega is a quasicircle. In particular, our results generalize the boundary Harnack inequalities in [BL] and [LN2] to operators with variable coefficients.

  • 24.
    Lundström, Niklas L.P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Olofsson, Marcus
    Önskog, Thomas
    Existence, uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching2019In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 475, no 1, p. 13-31Article in journal (Refereed)
    Abstract [en]

    We study viscosity solutions to a system of nonlinear degenerate parabolic partial integrodifferential equations with interconnected obstacles. This type of problem occurs in the context of optimal switching problems when the dynamics of the underlying state variable is described by an n-dimensional L´evy process. We first establish a continuous dependence estimate for viscosity sub- and supersolutions to the system under mild regularity, growth and structural assumptions on the partial integro-differential operator and on the obstacles and terminal conditions. Using the continuous dependence estimate, we obtain the comparison principle and uniqueness of viscosity solutions as well as Lipschitz regularity in the spatial variables. Our main contribution is construction of suitable families of viscosity sub- and supersolutions which we use as “barrier functions” to prove Ho¨lder continuity in the time variable, and, through Perron’s method, existence of a unique viscosity solution. This paper generalizes parts of the results of Biswas, Jakobsen and Karlsen (2010) and of Lundström, Nyström and Olofsson (2014) to hold for more general systems of equations.

  • 25.
    Lundström, Niklas L.P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vasilis, Jonatan
    Decay of a p-harmonic measure in the plane2013In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, p. 351-366Article in journal (Refereed)
    Abstract [en]

    We study the asymptotic behaviour of a p-harmonic measure w(p), p is an element of (1, infinity], in a domain Omega subset of R-2, subject to certain regularity constraints. Our main result is that w(p) (B (w, delta) boolean AND partial derivative Omega, w(0)) approximate to delta(q) as delta -> 0(+), where q = q(v,p) is given explicitly as a function of v and p. Here, v is related to properties of Omega near w. If p = infinity, this extends to some domains in R-n. By a result due to Hirata, our result implies that the p-Green function for p is an element of (1, 2) is not quasi-symmetric in plane C-1,C-1-domains.

  • 26.
    Lundström, Niklas
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Uppsala Univ, Dept Math.
    Olofsson, Marcus
    Uppsala Univ, Dept Math.
    Systems of variational inequalities for non-local operators related to optimal switching problems: existence and uniqueness2014In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 145, no 3-4, p. 407-432Article in journal (Refereed)
  • 27.
    Lundström, Niklas
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Söderbacka, Gunnar
    Estimates of size of cycle in a predator-prey system2018In: Differential Equations and Dynamical Systems, ISSN 0971-3514, E-ISSN 0974-6870Article in journal (Refereed)
    Abstract [en]

    We consider a Rosenzweig–MacArthur predator-prey system which incorporates logistic growth of the prey in the absence of predators and a Holling type II functional response for interaction between predators and preys. We assume that parameters take values in a range which guarantees that all solutions tend to a unique limit cycle and prove estimates for the maximal and minimal predator and prey population densities of this cycle. Our estimates are simple functions of the model parameters and hold for cases when the cycle exhibits small predator and prey abundances and large amplitudes. The proof consists of constructions of several Lyapunov-type functions and derivation of a large number of non-trivial estimates which are of independent interest.

  • 28.
    Lundström, Niklas
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Önskog, Thomas
    Department of Mathematics, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden.
    Stochastic and partial differential equations on non-smooth time-dependent domains2019In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 129, no 4, p. 1097-1131Article in journal (Refereed)
    Abstract [en]

    In this article, we consider non-smooth time-dependent domains whose boundary is W1,p in time and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. Secondly, we prove, using the theory of viscosity solutions, a comparison principle for fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. As a consequence, we obtain uniqueness, and, by barrier construction and Perron’s method, we also conclude existence of viscosity solutions. Our results generalize two articles by Dupuis and Ishii to time-dependent domains.

  • 29.
    Meng, Xinzhu
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bodin, Mats
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Dynamics and management of stage-structured fish stocks2013In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 75, no 1, p. 1-23Article in journal (Refereed)
    Abstract [en]

    With increasing fishing pressures having brought several stocks to the brink of collapse, there is a need for developing efficient harvesting methods that account for factors beyond merely yield or profit. We consider the dynamics and management of a stage-structured fish stock. Our work is based on a consumer-resource model which De Roos et al. (in Theor. Popul. Biol. 73, 47-62, 2008) have derived as an approximation of a physiologically-structured counterpart. First, we rigorously prove the existence of steady states in both models, that the models share the same steady states, and that there exists at most one positive steady state. Furthermore, we carry out numerical investigations which suggest that a steady state is globally stable if it is locally stable. Second, we consider multiobjective harvesting strategies which account for yield, profit, and the recovery potential of the fish stock. The recovery potential is a measure of how quickly a fish stock can recover from a major disturbance and serves as an indication of the extinction risk associated with a harvesting strategy. Our analysis reveals that a small reduction in yield or profit allows for a disproportional increase in recovery potential. We also show that there exists a harvesting strategy with yield close to the maximum sustainable yield (MSY) and profit close to that associated with the maximum economic yield (MEY). In offering a good compromise between MSY and MEY, we believe that this harvesting strategy is preferable in most instances. Third, we consider the impact of harvesting on population size structure and analytically determine the most and least harmful harvesting strategies. We conclude that the most harmful harvesting strategy consists of harvesting both adults and juveniles, while harvesting only adults is the least harmful strategy. Finally, we find that a high percentage of juvenile biomass indicates elevated extinction risk and might therefore serve as an early-warning signal of impending stock collapse.

1 - 29 of 29
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