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  • 1.
    Abbas, Qaisar
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

  • 2.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed)
  • 3.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008In: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, p. 52-62Conference paper (Other academic)
  • 4.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 5.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Faculty of Engineering Technology, University of Twente, AE Enschede, The Netherlands.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy Stability of the MUSCL Scheme2010In: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, p. 65:1-8Conference paper (Other academic)
  • 6.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy stability of the MUSCL scheme2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper (Refereed)
  • 7.
    Altafini, Claudio
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    The Geometric Phase of Stock Trading2016In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 11, no 8, p. e0161538-Article in journal (Refereed)
    Abstract [en]

    Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

  • 8.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Energy Stable Model Reduction of Neurons by Non-negative Discrete Empirical Interpolation2016In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, no 2, p. B297-B326Article in journal (Refereed)
    Abstract [en]

    The accurate and fast prediction of potential propagation in neuronal networks is of prime importance in neurosciences. This work develops a novel structure-preserving model reduction technique to address this problem based on Galerkin projection and nonnegative operator approximation. It is first shown that the corresponding reduced-order model is guaranteed to be energy stable, thanks to both the structure-preserving approach that constructs a distinct reduced-order basis for each cable in the network and the preservation of nonnegativity. Furthermore, a posteriori error estimates are provided, showing that the model reduction error can be bounded and controlled. Finally, the application to the model reduction of a large-scale neuronal network underlines the capability of the proposed approach to accurately predict the potential propagation in such networks while leading to important speedups.

  • 9.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 252, p. 573-590Article in journal (Refereed)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin–Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

  • 10.
    Andersson Granberg, Tobias
    et al.
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Norin, Anna
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Värbrand, Peter
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Yuan, Di
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Integrating optimization and simulation to gain more efficient airport logistics2009In: Eighth USA/Europe Air Traffic Management Research and Development Seminar (ATM2009), 2009, p. 1-10Conference paper (Refereed)
    Abstract [en]

    In this paper we present airport logistics, which is a framework of resource management in the air transportation system. Focus is on the processes supporting turn-around. A detailed simulation model of various processes involved in turn-around is developed, by which the interaction between these processes are analyzed. We show that integrating optimization and simulation is a powerful tool to demonstrate efficiency improvements in airport logistics, using scheduling de-icing trucks as an example. An optimization algorithm for scheduling de-icing trucks is developed and simulations are performed comparing different schedules. The schedule obtained when considering total airport performance in the optimization algorithm gives minimum flight delay and waiting times in the simulations.

  • 11.
    Andersson, Henrik
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Coordinated Routing: applications in location and inventory management2006Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Almost everywhere, routing plays an important role in everyday life. This thesis consists of three parts, each studying different applications where routing decisions are coordinated with other decisions. A common denominator in all applications is that an intelligent utilization of a fleet of vehicles is crucial for the performance of the system. In the first part, routing and inventorymanagement decisions are coordinated, in the second part, routing decisions concerning different modes of transportation are coordinated with inventory management, and in the third part, location decision and routing are coordinated.

    In the first part, an application concerning waste management is presented. Many industries generate garbage, and instead of handling the waste disposal themselves, other companies, specialized in garbage collection, handle the disposal. Each industry rents containers from a company to be used for waste, and the garbage collection companies handle the collection. The industries buy a service including one or more containers at the industry and the garbage collection companies are obliged to make sure that the containers never become overfull. The idea is that the industries buy this service and in return, the garbage collection company can plan the collection so that the overall cost and the number of overfull containers is minimized. Two models for the problem facing the garbage collection company are proposed. The first is solved using a Lagrangean relaxation approach on a flow based model, and the second is solved using Benders decomposition on a column based model.

    The second part investigates a distribution chain management problem taken from the Swedish pulp industry. Given fixed production plans at the mills, and fixed customer demands, the problem is to minimize the distribution cost. Unlike many other models for marine distribution chains, the customers are not located at the harbors. This means that the model proposed also incorporates the distribution planning from the harbors to the customers. All customers are not served from the harbors; some are served directly from the mills using trucks and trains to distribute the pulp, and these decisions are also included. The problem is modeled as a mixed integer linear program and solved using a branch and price scheme. Due to the complexity of the problem, the solution strategy is divided into two phases, where the first emphasizes the generation of schedules for the vessels operated by the company, while the second deals with the chartering of vessels on the spot market.

    In the third part, routing is combined with location decisions in the location-routing problem. Special emphasis is given to strategic management where decision makers must make location, capacity and routing decisions over a long planning period. The studied application comes fromstrategic schoolmanagement, where the location and capacity of the schools as well as their catchment areas are under consideration. The problem is modeled as a mixed integer linear program. The computational study shows the importance of incorporating

    a routing component allowing multiple visits, as well as the danger of having a too short planning period.

    List of papers
    1. A Lagrangean Based Heuristic for the Inventory Routing Problem
    Open this publication in new window or tab >>A Lagrangean Based Heuristic for the Inventory Routing Problem
    2006 (English)In: European Journal of Operational Research, ISSN 0377-2217Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13900 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    2. A pseudo Benders Decomposition Approach
    Open this publication in new window or tab >>A pseudo Benders Decomposition Approach
    2002 (English)In: Proceedings of Nordic MPS ’02, 2002Conference paper, Published paper (Other academic)
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13901 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    3. A Distribution Chain Management Problem in the Swedish Pulp Industry
    Open this publication in new window or tab >>A Distribution Chain Management Problem in the Swedish Pulp Industry
    2006 (English)Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13902 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    4. Decision Support for Distribution Chain Management: the Swedish Pulp Industry
    Open this publication in new window or tab >>Decision Support for Distribution Chain Management: the Swedish Pulp Industry
    2004 (English)In: 7th International Conference on Intelligent Transport Systems, 2004, p. 1051-1056Conference paper, Published paper (Other academic)
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13903 (URN)
    Available from: 2006-07-12 Created: 2006-07-12 Last updated: 2009-04-23
    5. Location-Routing Problems: An Annotated Bibliography
    Open this publication in new window or tab >>Location-Routing Problems: An Annotated Bibliography
    2006 (English)Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13904 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
    6. The Relocation-Routing Problem
    Open this publication in new window or tab >>The Relocation-Routing Problem
    2006 (English)Article in journal (Refereed) Submitted
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-13905 (URN)
    Available from: 2006-07-12 Created: 2006-07-12
  • 12.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Pinto da Costa, A.
    University of Lisbon, Portugal.
    Agwa, M. A.
    Zagazig University, Egypt.
    Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds2016In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, no 1, p. 78-105Article in journal (Refereed)
    Abstract [en]

    We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

  • 13.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Global search strategies for solving multilinear least-squares problems2012In: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, no 1, p. 12-21Article in journal (Refereed)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

  • 14.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Global Search Strategies for Solving Multilinear Least-squares Problems2011Report (Other academic)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinearoperator is used in place of a matrix-vector product. The MLLS istypically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.

  • 15.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2013Report (Other academic)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 16.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2015In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, no 2, p. 259-277Article in journal (Refereed)
    Abstract [en]

    Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.

    An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 17.
    Andersson, Per-Åke
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Multi-year maintenance optimisation for paved public roads - segment based modelling and price-directive decomposition2007Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The thesis deals with the generation of cost efficient maintenance plans for paved roads, based on database information about the current surface conditions and functional models for costs and state changes, partly developed in cooperation with Vägverket (VV, Swedish Road Administration). The intended use is in a stage of budgeting and planning, before concrete project information is available. Unlike the up to now used models, individual maintenance plans can be formulated for each segment (a homogeneous road section as to the current pavement state and paving history), in continuous state and works spaces. By using Lagrangean relaxation optimisation techniques, the special benefit/cost-ratio constraints that VV puts on each maintenance project can be naturally mastered by dual prices for the budget constraints. The number of segments competing for budget resources is usually large. Data from VV Vägdatabank (SRA Road Database) in county Värmland were used, comprising around 9000 road segments. Due to the large data amount the implemented programs rely on parallel computation. During the thesis work, access to the PC-cluster Monolith at NSC was granted. In order to reduce optimisation run times, model & method development was needed. By aggregating the road segments into road classes, good initial values of the dual prices were achieved. By adding new state dimensions, the use of the Markov property could be motivated. By developing a special residual value routine, the explicitly considered time period could be reduced. At solving the dual subproblem special attention was paid to the discretization effects in the dynamic programming approach. One type of study is on a sub-network, e.g. a road. Validation studies were performed on road 63 in Värmland – with promising but not satisfactory results (see below). A special model for co-ordinated maintenance considers the fine-tuned cost effects of simultaneous maintenance of contiguous road segments. The other main type of study is for a whole network. Several method types have been applied, both for solving the relaxed optimisation problems and for generating maintenance plans that fit to the budgets. For a decent discretization, the run time for the whole Värmland network is less than 80 CPU-hrs.A posterior primal heuristics reduces the demands for parallel processing to a small PC-cluster.The thesis further studies the effects of redistributing budget means, as well as turning to a transparent stochastic model – both showing modest deviations from the basic model.

    Optimisation results for Värmland indicate budget levels around 40% of the actual Värmland budget as sufficient. However, important cost triggers are missing in this first model round, e.g., certain functional performance (safety), all environmental performance (noise etc.) and structural performance (e.g. bearing capacity, only modelled by an age measure). For increased credibility of PMS in general and optimisation in particular, the discrepancies should be further analysed and lead to improvements as to condition monitoring, state effect & cost modelling and mathematical modelling & implementation.

  • 18.
    Arndt, Carl-Fredrik
    Linköping University, Department of Mathematics, Scientific Computing.
    Energy estimates and variance estimation for hyperbolic stochastic partial differentialequations2011Independent thesis Advanced level (professional degree), 30 credits / 45 HE creditsStudent thesis
    Abstract [en]

    In this thesis the connections between the boundary conditions and the vari- ance of the solution to a stochastic partial differential equation (PDE) are investigated. In particular a hyperbolical system of PDE’s with stochastic initial and boundary data are considered. The problem is shown to be well- posed on a class of boundary conditions through the energy method. Stability is shown by using summation-by-part operators coupled with simultaneous- approximation-terms. By using the energy estimates, the relative variance of the solutions for different boundary conditions are analyzed. It is concluded that some types of boundary conditions yields a lower variance than others. This is verified by numerical computations.

  • 19.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden .
    Bordemann, Martin
    Laboratoire de MIA, 4 rue des Frères Lumière, Univ. deHaute-Alsace, 68093, Mulhouse, France .
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden .
    Lee, Choonkyu
    Department of Physics and Center for Theoretical Physics, Seoul National University, 151-747, Seoul, South Korea .
    Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics2008In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 84, p. 89-98Article in journal (Refereed)
    Abstract [en]

    We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.

  • 20.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Choe, Jaigyoung
    Korea Institute Adv Study, South Korea.
    Hoppe, Jens
    Royal Institute Technology, Sweden.
    Noncommutative Minimal Surfaces2016In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, no 8, p. 1109-1129Article in journal (Refereed)
    Abstract [en]

    We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.

  • 21.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, Stockholm, 100 44, Sweden .
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, Stockholm, 100 44, Sweden .
    EIGENVALUE DYNAMICS, FOLLYTONS AND LARGEN LIMITS OF MATRICES2006In: Applications of Random Matrices in Physics / [ed] Édouard Brézin, Vladimir Kazakov, Didina Serban, Paul Wiegmann, Anton Zabrodin, Springer, 2006, 211, p. 89-94Chapter in book (Refereed)
    Abstract [en]

    How do the eigenvalues of a “free” hermitian N × N matrix X(t) evolve in time? The answer is provided by the rational Calogero-Moser systems [5, 13] if (!) the initial conditions are chosen such that i[X(0),Ẋ(0)] has a non-zero eigenvalue of multiplicity N–1; for generic X(0),Ẋ(0) the question remained unanswered for 30 years.

  • 22.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
    Eigenvalue-Dynamics off the Calogero–Moser System2004In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, p. 121-129Article in journal (Refereed)
    Abstract [en]

    By finding N(N− 1)/2 suitable conserved quantities, free motions of real symmetric N×N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X – in contrast to the rational Calogero-Moser system, for which [X(0),Xd(0)] has to be purely imaginary, of rank one.

  • 23.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden.
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden.
    Theisen, Stefan
    Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany.
    Spinning membranes2004In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 599, no 1-2, p. 118-128Article in journal (Refereed)
    Abstract [en]

    We present new solutions of the classical equations of motion of bosonic (matrix-)membranes. Those relating to minimal surfaces in spheres provide spinning membrane solutions in AdSp×SqAdSp×Sq, as well as in flat space–time. Nontrivial reductions of the BMN matrix model equations are also given.

  • 24.
    Arnlind, Joakim
    et al.
    Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
    Mickelsson, Jouko
    Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
    Trace Extensions, Determinant Bundles, and Gauge Group Cocycles2002In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 62, no 2, p. 101-110Article in journal (Refereed)
    Abstract [en]

    We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.

  • 25.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On Production Planning and Activity Periods2015Report (Other academic)
    Abstract [en]

    Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

  • 26.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Production planning, activity periods and passivity periods2015Report (Other academic)
    Abstract [en]

    Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

  • 27.
    Bartolini, Gabriel
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera2009Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Compact Riemann surfaces of genus greater than 1 can be realized as quotient spaces of the hyperbolic plane by the action of Fuchsian groups. The Teichmüller space is the set of all complex structures of Riemann surfaces and the moduli space the set of conformal equivalence classes of Riemann surfaces. For genus greater than two the branch locus of the covering of the moduli space by the Teichmüller space can be identified wi the set of Riemann surfaces admitting non-trivial automorphisms. Here we give the orbifold structure of the branch locus of surfaces of genus 5 by studying the equisymmetric stratification of the branch locus. This gives the orbifold structure of the moduli space.

    We also show that the strata corresponding to surfaces with automorphisms of order 2 and 3 belong to the same connected component for every genus. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.

    List of papers
    1. ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 4
    Open this publication in new window or tab >>ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 4
    2010 (English)In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 52, p. 401-408Article in journal (Refereed) Published
    Abstract [en]

    Let g be an integer ≥ 3 and let θg = {X ∈ Mg|Aut(X) ≠ 1d}, where Mg denotes the moduli space of a compact Riemann surface. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belongs to the same connected component. We also prove the connectedness of θg for g = 5, 6, 7 and 8 with the exception of the isolated points given by Kulkarni.

    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-51518 (URN)10.1017/S0017089510000091 (DOI)000277348200016 ()
    Note

    Original Publication: Gabriel Bartolini and Milagros Izquierdo, On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus, 2010, Glasgow Mathematical Journal, (52), 401-408. http://dx.doi.org/10.1017/S0017089510000091 Copyright: Cambridge University Press http://www.cambridge.org/uk/

    Available from: 2009-11-05 Created: 2009-11-05 Last updated: 2017-12-12Bibliographically approved
  • 28.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 42010In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 52, p. 401-408Article in journal (Refereed)
    Abstract [en]

    Let g be an integer ≥ 3 and let θg = {X ∈ Mg|Aut(X) ≠ 1d}, where Mg denotes the moduli space of a compact Riemann surface. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belongs to the same connected component. We also prove the connectedness of θg for g = 5, 6, 7 and 8 with the exception of the isolated points given by Kulkarni.

  • 29.
    Beckius, Peter
    et al.
    Linköping University, Department of Management and Engineering.
    Hübel, Alexander
    Linköping University, Department of Management and Engineering.
    Vädrets påverkan på försäljningen inom svensk dagligvaruhandel: En studie om vädrets påverkan på ICA:s försäljning2010Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [ar]

    ICA is the largest general dealer in the Swedish market as well as the largest supplier to the independent ICA-dealers. The principal and one of the biggest stakeholders of this thesis is the department Supply Chain Development who is responsible for the development of ICA’s Supply Chain.

    The purpose of this study is to examine how ICA’s sales are affected by weather and to make recommendations on how ICA should proceed with its work regarding this issue. By leveraging their forecasts by including weather, ICA hopes that their logistical metrics amount of spoilage, service levels and number of inventory days will improve. This thesis describes how ICA is working with weather currently, and furthermore it discusses the existing literature within this area. Extensive statistical surveys have been conducted in order to identify the products that are affected by weather, and to examine how they are affected by different weather variables. Finally, the thesis gives recommendations to ICA on how they can improve their forecasting by taking this study’s results into account.

    Presently ICA has no consistent approach when it comes to considering weather’s impact on sales. Each individual product planner uses his own experience and gut feeling and there is no central guidance or other quantitative information there to help them.

    This thesis is organised around two major statistical studies. First, a correlation study examines the correlation between sales and deviation from mean temperature. The weather parameter was selected following recommendations from earlier studies and from SMHI - the national weather institute in Sweden. The study was conducted on ICA’s entire assortment and identified which items that were affected by weather. These turned out to be about a hundred in number and were affected mainly during the summer; however a few items were also affected in the winter. Most of the affected items were rather logical regarding weather’s effects on sales and have also been pointed out by planners as products that are likely to be affected by weather. Following that, several regression analyses were conducted on the selected weather affected assortment.

    The regression analyses were conducted with various combinations of one or more weather parameters as explanatory variables. Surprisingly, in most cases the deviation from mean temperature alone was the parameter that best explained the variance in sales figures. The result or output of this thesis is a value for the expected change in sales for a selected assortment, given a change in deviation from mean temperature.

    The recommendations given at the end of this thesis explains how ICA in a simple and cost effective way could implement the study's results in their daily work. The proposal is to divide the work by what should be done centrally by the forecasting department, and by what should be done individually by each planner. The forecasting department should regularly collect weather forecasts over different time periods, calculate the deviation from mean temperature and distribute it to the supply planner. After that, it is up to the supply planners on how to best take advantage of this information by taking into account other unique factors affecting each category, such as campaigns, holidays and daily indexes that in many cases have more effect on sales than the weather.

  • 30.
    Bengtsson, Martin
    Linköping University, Department of Mathematics.
    Analytical Expressions for the Hawking Mass in slowly rotating Kerr and Kerr-Newman Space-times2007Independent thesis Advanced level (degree of Magister), 20 points / 30 hpStudent thesis
    Abstract [en]

    Penrose's inequality which relates the total mass of a space-time containing a black hole with the area of the event horizon, is a yet unproven condition that is required for the cosmic censorship hypothesis. It is believed that the inequality could be proved by using properties of the Hawking mass. This thesis gives analytical expressions for the Hawking mass in slowly rotating Kerr and Kerr-Newman space-times. It is also shown that the expressions are monotonically increasing, a result that does not contradict Penrose's inequality.

  • 31.
    Berg, Jens
    Uppsala universitet, Avdelningen för beräkningsvetenskap.
    Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems2013Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids and electromagnetic waves to the stock market and traffic jams. There are many methods for numerically approximating solutions to PDEs. Some of the most commonly used ones are the finite volume method, the finite element method, and the finite difference method. All methods have their strengths and weaknesses, and it is the problem at hand that determines which method that is suitable. In this thesis, we focus on the finite difference method which is conceptually easy to understand, has high-order accuracy, and can be efficiently implemented in computer software.

    We use the finite difference method on summation-by-parts (SBP) form, together with a weak implementation of the boundary conditions called the simultaneous approximation term (SAT). Together, SBP and SAT provide a technique for overcoming most of the drawbacks of the finite difference method. The SBP-SAT technique can be used to derive energy stable schemes for any linearly well-posed initial boundary value problem. The stability is not restricted by the order of accuracy, as long as the numerical scheme can be written in SBP form. The weak boundary conditions can be extended to interfaces which are used either in domain decomposition for geometric flexibility, or for coupling of different physics models.

    The contributions in this thesis are twofold. The first part, papers I-IV, develops stable boundary and interface procedures for computational fluid dynamics problems, in particular for problems related to the Navier-Stokes equations and conjugate heat transfer. The second part, papers V-VI, utilizes duality to construct numerical schemes which are not only energy stable, but also dual consistent. Dual consistency alone ensures superconvergence of linear integral functionals from the solutions of SBP-SAT discretizations. By simultaneously considering well-posedness of the primal and dual problems, new advanced boundary conditions can be derived. The new duality based boundary conditions are imposed by SATs, which by construction of the continuous boundary conditions ensure energy stability, dual consistency, and functional superconvergence of the SBP-SAT schemes.

  • 32.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    A stable and dual consistent boundary treatment using finite differences on summation-by-parts form2012In: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna University of Technology , 2012Conference paper (Other academic)
    Abstract [en]

    This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-posed and the discrete problem is stable and spatially dual consistent. These two features result in a superconvergent functional, in the sense that the order of accuracy of the functional is provably higher than that of the solution.

  • 33.
    Berg, Jens
    et al.
    Uppsala University, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations2014In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 259, p. 135-153Article in journal (Refereed)
    Abstract [en]

    In this paper we derive new farfield boundary conditions for the time-dependent Navier–Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier–Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations.

    We perform computations with a high-order finite difference scheme on summation-by-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent.

  • 34.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Duality based boundary treatment for the Euler and Navier-Stokes equations2013In: AIAA Aerospace Sciences - Fluid Sciences Event, 2013, p. 1-19Conference paper (Other academic)
    Abstract [en]

    In this paper we construct well-posed boundary conditions for the compressible Euler and Navier-Stokes equations in two space dimensions. When also considering the dual equations, we show how to construct the boundary conditions so that both the primal and dual problems are well-posed. By considering the primal and dual problems simultaneously, we construct energy stable and dual consistent finite difference schemes on summation-by-  parts form with weak imposition of the boundary conditions.

    According to linear theory, the stable and dual consistent discretization can be used to compute linear integral functionals from the solution at a superconvergent rate. Here we evaluate numerically the superconvergence property for the non-linear Euler and Navier{ Stokes equations with linear and non-linear integral functionals.

  • 35.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, SE-751 05, Uppsala, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    On the impact of boundary conditions on dual consistent finite difference discretizations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 236, p. 41-55Article in journal (Refereed)
    Abstract [en]

    In this paper we derive well-posed boundary conditions for a linear incompletely parabolic system of equations, which can be viewed as a model problem for the compressible Navier{Stokes equations. We show a general procedure for the construction of the boundary conditions such that both the primal and dual equations are wellposed.

    The form of the boundary conditions is chosen such that reduction to rst order form with its complications can be avoided.

    The primal equation is discretized using finite difference operators on summation-by-parts form with weak boundary conditions. It is shown that the discretization can be made energy stable, and that energy stability is sufficient for dual consistency.

    Since reduction to rst order form can be avoided, the discretization is significantly simpler compared to a discretization using Dirichlet boundary conditions.

    We compare the new boundary conditions with standard Dirichlet boundary conditions in terms of rate of convergence, errors and discrete spectra. It is shown that the scheme with the new boundary conditions is not only far simpler, but also has smaller errors, error bounded properties, and highly optimizable eigenvalues, while maintaining all desirable properties of a dual consistent discretization.

  • 36.
    Berg, Jens
    et al.
    Division of Scientific Computing, Department of Information Technology, Uppsala University, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains2012In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 62, no 11, p. 1620-1638Article in journal (Refereed)
    Abstract [en]

    In this paper we study the heat and advectionequation in single and multipledomains. The equations are discretized using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices.

    It is shown how the spectrum of the singledomain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. The interface treatments are posed as a function of one parameter, and the impact on the spectrum and discretization error is investigated as a function of this parameter. Finally we briefly discuss the generalization to higher order accurate schemes.

  • 37.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Scientific Computing.
    Stable Robin solid wall boundary conditions for the Navier-Stokes equations2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 19, p. 7519-7532Article in journal (Refereed)
    Abstract [en]

    In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier–Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters.

    The discretization is done using finite differences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of flows ranging from no-slip to almost full slip.

  • 38.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, no 20, p. 6846-6860Article in journal (Refereed)
    Abstract [en]

    Finitedifference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT).

    In general, an SBP-SAT discretization is accurate of order p + 1 with an internal accuracy of 2p and a boundary accuracy of p. Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way.

    The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergentfunctionaloutputs.

  • 39. Berggren, Martin
    et al.
    Ekström, Sven-Erik
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method2009In: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, p. 456-468Article in journal (Refereed)
  • 40.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Designing, implementing and evaluating mathematical modelling modules at the upper secondary level2009Report (Other academic)
    Abstract [en]

    This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.

    The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.

    The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.

    It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.

  • 41.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-20002009Report (Other academic)
    Abstract [en]

    Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.

  • 42.
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Computationel Mathematics. Linköping University, The Institute of Technology.
    An Inverse Heat Conduction Problem and Improving Shielded Thermocouple Accuracy2012In: Numerical Heat Transfer, Part A Applications, ISSN 1040-7782, E-ISSN 1521-0634, Vol. 61, no 10, p. 754-763Article in journal (Refereed)
    Abstract [en]

    A shielded thermocouple is a measurement device used for monitoring the temperature in chemically, or mechanically, hostile environments. The sensitive parts of the thermocouple are protected by a shielding layer. In order to improve the accuracy of the measurement device, we study an inverse heat conduction problem where the temperature on the surface of the shielding layer is sought, given measured temperatures in the interior of the thermocouple. The procedure is well suited for real-time applications where newly collected data is continuously used to compute current estimates of the surface temperature. Mathematically we can formulate the problem as a Cauchy problem for the heat equation, in cylindrical coordinates, where data is given along the line r = r 1 and the solution is sought at r 1 < r ≤ r 2. The problem is ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. Thus, regularization techniques are needed. The ill–posedness of the problem is analyzed and a numerical method is proposed. Numerical experiments demonstrate that the proposed method works well.

  • 43.
    Berntsson, Fredrik
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Eldén, Lars
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Numerical Solution of Cauchy Problems for Elliptic Equations in ``Rectangle-like'' Geometries2005In: Proceedings for the FEMLAB Conference 2005, 2005Conference paper (Other academic)
    Abstract [en]

    We consider two dimensional inverse steady state heat conductionproblems in complex geometries. The coefficients of the elliptic equation are assumed to be non-constant. Cauchy data are given on onepart of the boundary and we want to find the solution in the wholedomain. The problem is ill--posed in the sense that the solution doesnot depend continuously on the data.

    Using an orthogonal coordinate transformation the domain is mappedonto a rectangle. The Cauchy problem can then be solved by replacing one derivative by a bounded approximation. The resulting well--posed problem can then be solved by a method of lines. A bounded approximation of the derivative can be obtained by differentiating a cubic spline, that approximate the function in theleast squares sense. This particular approximation of the derivativeis computationally efficient and flexible in the sense that its easy to handle different kinds of boundary conditions.This inverse problem arises in iron production, where the walls of amelting furnace are subject to physical and chemical wear. Temperature and heat--flux data are collected by several thermocouples locatedinside the walls. The shape of the interface between the molten ironand the walls can then be determined by solving an inverse heatconduction problem.  In our work we make extensive use of Femlab for creating testproblems. By using FEMLAB we solve relatively complex model problems for the purpose of creating numerical test data used for validating our methods. For the types of problems we are intressted in numerical artefacts appear, near corners in the domain, in the gradients that Femlab calculates. We demonstrate why this happen and also how we deal with the problem.

  • 44.
    Berntsson, Fredrik
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Karlsson, Matts
    Linköping University, Department of Management and Engineering, Applied Thermodynamics and Fluid Mechanics. Linköping University, Faculty of Science & Engineering.
    Kozlov, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Nazarov, Sergey A.
    St Petersburg State University, St Petersburg State Polytechnical University, and Institute of Problems of Mechanical Engineering RAS, Russia..
    A one-dimensional model of a false aneurysm2017In: International Journal of Research in Engineering and Science (IJRES), ISSN 2320-9356, Vol. 5, no 6, p. 61-73Article in journal (Refereed)
    Abstract [en]

     A false aneurysm is a hematoma, i.e. collection ofblood outside of a blood vessel, that forms due to a hole  in the wall of an artery . This represents a serious medical condition that needs to be monitored and, under certain conditions, treatedurgently. In this work a one-dimensional model of a false aneurysm isproposed. The new model is based on a one-dimensional model of anartery previously presented by the authors and it takes into accountthe interaction between the hematoma  and the surrounding musclematerial. The model equations are derived  using rigorous asymptoticanalysis for the case of a simplified geometry.   Even though the model is simple it still supports a realisticbehavior for the system consisting of the vessel and the  hematoma. Using numerical simulations we illustrate the behavior ofthe model. We also investigate the effect  of changing the size of the hematoma. The simulations show that ourmodel can reproduce realistic solutions. For instance we show thetypical strong pulsation of an aneurysm by blood entering the hematoma during the work phase of the cardiac cycle, and the blood returning tothe vessel during the resting phase. Also we show that the aneurysmgrows  if the pulse rate is increased due to, e.g., a higher work load. 

  • 45.
    Berntsson, Fredrik
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Kozlov, Vladimir A.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Mpinganzima, Lydie
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. University of Rwanda.
    Turesson, Bengt-Ove
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Numerical Solution of the Cauchy Problem for the Helmholtz Equation2014Report (Other academic)
    Abstract [en]

    The Cauchy problem for the Helmholtz equation appears in applications related to acoustic or electromagnetic wave phenomena. The problem is ill–posed in the sense that the solution does not depend on the data in a stable way. In this paper we give a detailed study of the problem. Specifically we investigate how the ill–posedness depends on the shape of the computational domain and also on the wave number. Furthermore, we give an overview over standard techniques for dealing with ill–posed problems and apply them to the problem.

  • 46.
    Berntsson, Fredrik
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Kozlov, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Mpinganzima, L.
    University of Rwanda, Rwanda.
    Turesson, Bengt-Ove
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Iterative Tikhonov regularization for the Cauchy problem for the Helmholtz equation2017In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 73, no 1, p. 163-172Article in journal (Refereed)
    Abstract [en]

    The Cauchy problem for the Helmholtz equation appears in various applications. The problem is severely ill-posed and regularization is needed to obtain accurate solutions. We start from a formulation of this problem as an operator equation on the boundary of the domain and consider the equation in (H-1/2)* spaces. By introducing an artificial boundary in the interior of the domain we obtain an inner product for this Hilbert space in terms of a quadratic form associated with the Helmholtz equation; perturbed by an integral over the artificial boundary. The perturbation guarantees positivity property of the quadratic form. This inner product allows an efficient evaluation of the adjoint operator in terms of solution of a well-posed boundary value problem for the Helmholtz equation with transmission boundary conditions on the artificial boundary. In an earlier paper we showed how to take advantage of this framework to implement the conjugate gradient method for solving the Cauchy problem. In this work we instead use the Conjugate gradient method for minimizing a Tikhonov functional. The added penalty term regularizes the problem and gives us a regularization parameter that can be used to easily control the stability of the numerical solution with respect to measurement errors in the data. Numerical tests show that the proposed algorithm works well. (C) 2016 Elsevier Ltd. All rights reserved.

    The full text will be freely available from 2018-12-01 14:25
  • 47.
    Berntsson, Fredrik
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mpinganzima, Lydie
    National University of Rwanda, Box 117, Butare, Rwanda.
    A Data Assimilation Approach to Coefficient Identification2011Report (Other academic)
    Abstract [en]

    The thermal conductivity properties of a material can be determined experimentally by using temperature measurements taken at specified locations inside the material. We examine a situation where the properties of a (previously known) material changed locally. Mathematically we aim to find the coefficient k(x) in the stationary heat equation (kTx)x = 0;under the assumption that the function k(x) can be parametrized using only a few degrees of freedom.

    The coefficient identification problem is solved using a least squares approach; where the (non-linear) control functional is weighted according to the distribution of the measurement locations. Though we only discuss the 1D case the ideas extend naturally to 2D or 3D. Experimentsdemonstrate that the proposed method works well.

     

     

     

     

  • 48.
    Berntsson, Fredrik
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Orlof, Anna
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Thim, Johan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Error Estimation for Eigenvalues of Unbounded Linear Operators and an Application to Energy Levels in Graphene Quantum Dots2017In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 38, no 3, p. 293-305Article in journal (Refereed)
    Abstract [en]

    The eigenvalue problem for linear differential operators is important since eigenvalues correspond to the possible energy levels of a physical system. It is also important to have good estimates of the error in the computed eigenvalues. In this work, we use spline interpolation to construct approximate eigenfunctions of a linear operator using the corresponding eigenvectors of a discretized approximation of the operator. We show that an error estimate for the approximate eigenvalues can be obtained by evaluating the residual for an approximate eigenpair. The interpolation scheme is selected in such a way that the residual can be evaluated analytically. To demonstrate that the method gives useful error bounds, we apply it to a problem originating from the study of graphene quantum dots where the goal was to investigate the change in the spectrum from incorporating electron–electron interactions in the potential.

  • 49.
    Björck, Åke
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Numerical methods in matrix computations2014 (ed. 1)Book (Refereed)
  • 50.
    Blikstad, Mathias
    et al.
    Saab AB, Sweden.
    Karlsson, Emil
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Lööw, Tomas
    Saab AB, Sweden.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    A constraint generation procedure for pre-runtime scheduling of integrated modular avionic systems2017In: Proceedings of the 13th Workshop on Models and Algorithms for Planning and Scheduling Problems / [ed] Susanne Albers, Nicole Megow, Andreas S. Schulz, Leen Stougie, 2017Conference paper (Other academic)
    Abstract [en]

    In modern integrated modular avionic systems, applications share hardware resources on a common avionic platform. Such an architecture necessitates strict requirements on the spatial and temporal partitioning of the system to prevent fault propagation between different aircraft functions. One way to establish a temporal partitioning is through pre-runtime scheduling of the system, which involves creating a schedule for both tasks and a communication network.

    While the avionic systems are growing more and more complex, so is the challenge of scheduling them. Scheduling of the system has an important role in the development of new avionic systems since functionality typically is added to the system over a period of several years and a scheduling tool is used both to detect if the platform can host the new functionality and, in case this is possible, to create a new schedule. For this reason an exact solution strategy for avionics scheduling is preferred over a heuristic one.

    In this paper we present a mathematical model for an industrially relevant avionic system and present a constraint generation  procedure for scheduling of such systems. We apply our optimisation approach to instances provided by our industrial partner. These instances are of relevance for the development of future avionic systems and contain up to 20 000 tasks to be scheduled. The computational results show that our optimisation approach can be used to create schedules for such instances within reasonable time.

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