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  • 1.
    Carlsen, Martin
    et al.
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Darula, Radoslav
    Aalborg University, Aalborg, Denmark.
    Gravesen, Jens
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Hjorth, Poul G.
    Dynamical systems, Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Jørgensen, H. B.
    University of Southern Denmark, Odense, Denmark.
    Nguyen, Dang Manh
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Nielsen, Peter Nørtoft
    Geometry, Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Olsen, J.
    Joltech, Sønderborg, Denmark.
    Petersen, H. G.
    University of Southern Denmark, Odense, Denmark.
    Røgen, Peter
    Geometry, Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Ögren, Magnus
    Department of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    Efficiency of a gyroscopic device for conversion of mechanical wave energy to electric energy: Technical report from ESGI-83 workshop in industrial mathematics 20112011Report (Other academic)
    Abstract [en]

    We consider a recently proposed gyroscopic device for conversion of mechanical ocean wave energy to electrical energy. Two models of the device derived from standard engineering mechanics from the literature are analysed, and a model is derived from analytical mechanics considerations. From these models, estimates of the power production, efficiency, forces and moments are made. We find that it is possible to extract a significant amount of energy from an ocean wave using the described device. Further studies are required for a full treatment of the device.

  • 2.
    Cheng, Xiaoliang
    et al.
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Lin, Guangliang
    Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Zhang, Ye
    Örebro University, School of Science and Technology. Department of Mathematics.
    Gong, Rongfang
    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology. Department of Mathematics.
    A modified coupled complex boundary method for an inverse chromatography problem2018In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 26, no 1, p. 33-49Article in journal (Refereed)
    Abstract [en]

    Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

  • 3.
    Corboz, Philippe
    et al.
    School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Ögren, Magnus
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Kheruntsyan, Karén
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Corney, Joel F.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, The University of Queensland, Brisbane Qld, Australia.
    Phase-space methods for fermions2013In: Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics / [ed] Davis, M.; Gardiner, S.; Proukakis, N.; Szymańska, M., London: Imperial College Press, 2013, p. 407-416Chapter in book (Other academic)
    Abstract [en]

    We review phase-space simulation techniques for fermions, showing how a Gaussian operator basis leads to exact calculations of the evolution of a many-body quantum system in both real and imaginary time. We apply such techniques to the Hubbard model and to the problem of molecular dissociation of bosonic molecules into pairs of fermionic atoms.

  • 4.
    Dai, Xiaoxia
    et al.
    School of Computing Science, Zhejiang University City College, Hangzhou, Zhejiang, People’s Republic of China.
    Zhang, Chengwei
    School of Computing Science, Zhejiang University City College, Hangzhou, Zhejiang, People’s Republic of China.
    Zhang, Ye
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method2017In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488Article in journal (Refereed)
    Abstract [en]

    This paper presents a piecewise constant level set method for the topology optimization of steady Navier- Stokes flow. Combining piecewise constant level set functions and artificial friction force, the optimization problem is formulated and analyzed based on a design variable. The topology sensitivities are computed by the adjoint method based on Lagrangian multipliers. In the optimization procedure, the piecewise constant level set function is updated by a new descent method, without the needing to solve the Hamilton-Jacobi equation. To achieve optimization, the piecewise constant level set method does not track the boundaries between the different materials but instead through the regional division, which can easily create small holes without topological derivatives. Furthermore, we make some attempts to avoid updating the Lagrangian multipliers and to deal with the constraints easily. The algorithm is very simple to implement, and it is possible to obtain the optimal solution by iterating a few steps. Several numerical examples for both two- and three-dimensional problems are provided, to demonstrate the validity and efficiency of the proposed method.

  • 5.
    Gulliksson, Mårten
    et al.
    Örebro University, School of Science and Technology.
    Holmbom, Anders
    Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
    Persson, Jens
    Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
    Zhang, Ye
    Örebro University, School of Science and Technology.
    A separating oscillation method of recovering the G-limit in standard and non-standard homogenization problems2016In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 32, no 2, article id 025005Article in journal (Refereed)
    Abstract [en]

    Reconstructing the homogenized coefficient, which is also called the G-limit, in elliptic equations involving heterogeneous media is a typical nonlinear ill-posed inverse problem. In this work, we develop a numerical technique to determine G-limit that does not rely on any periodicity assumption. The approach is a technique that separates the computation of the deviation of the G-limit from the weak -limit of the sequence of coefficients from the latter. Moreover, to tackle the ill-posedness, based on the classical Tikhonov regularization scheme we develop several strategies to regularize the introduced method. Various numerical tests for both standard and non-standard homogenization problems are given to show the efficiency and feasibility of the proposed method.

  • 6.
    Gustafsson, Jonas
    et al.
    Örebro University, School of Science and Technology.
    Olofsson, Isac
    Örebro University, School of Science and Technology.
    RSA-kryptografi för gymnasiet2011Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna bok riktar sig till gymnasieelever som vill fördjupa sig i ämnet RSA-kryptografi . RSA-kryptografi är en avancerad metod för att kommunicera med hemliga meddelanden och används flitigt inom t.ex. bankvärlden. När du handlar med ditt kort eller använder din e-legitimation används RSA-kryptogra fi för att allt du gör ska vara skyddat och säkert. Vid stora transaktioner mellan olika banker används också RSA-kryptogra fi för att både den som betalar och den som får betalt ska vara säkra att allt går rätt till.Boken är uppdelad i fyra kapitel. Kapitel 3 och 4 är betydligt mer avancerade än kapitel 1 och 2. Kapitel 1 består mestadels av exempel och övningar som behandlar matematiken som krävs för att kunna utföra RSA-kryptogra fi med små tal. Kapitel 2 använder matematiken i kapitel 1 för att genom exempel och övingar metodiskt lära ut hur RSA-kryptogra fi med små tal går till. Kapitel 3 visar matematiken som ligger till grund för att RSA-kryptografi fungerar. Detta visas med hjälp av exempel, satser, förtydligade bevis samt några enstaka övningar. Kapitel 4 förklarar varför RSA-kryptografi är säkert och enkelt att använda. Primtalstester utgör det viktigaste ämnet i detta sista kapitel. 

  • 7.
    Lin, G.
    et al.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    Zhang, Ye
    Örebro University, School of Science and Technology. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Cheng, X.
    Department of Mathematics, Zhejiang University, Hangzhou, China.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Forssén, P.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Fornstedt, T.
    Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography2018In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 13-40Article in journal (Refereed)
    Abstract [en]

    Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.

  • 8.
    Lin, Guangliang
    et al.
    School of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Cheng, Xiaoliang
    School of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.
    Zhang, Ye
    Örebro University, School of Science and Technology. Faculty of Mathematics, Technische Universitat Chemnitz, Chemnitz, Germany.
    A parametric level set based collage method for an inverse problem in elliptic partial differential equations2018In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 340, p. 101-121Article in journal (Refereed)
    Abstract [en]

    In this work, based on the collage theorem, we develop a new numerical approach to reconstruct the locations of discontinuity of the conduction coefficient in elliptic partial differential equations (PDEs) with inaccurate measurement data and coefficient value. For a given conductivity coefficient, one can construct a contraction mapping such that its fixed point is just the gradient of a solution to the elliptic system. Therefore, the problem of reconstructing a conductivity coefficient in PDEs can be considered as an approximation of the observation data by the fixed point of a contraction mapping. By collage theorem, we translate it to seek a contraction mapping that keeps the observation data as close as possible to itself, which avoids solving adjoint problems when applying the gradient descent method to the corresponding optimization problem. Moreover, the total variation regularizing strategy is applied to tackle the ill-posedness and the parametric level set technique is adopted to represent the discontinuity of the conductivity coefficient. Various numerical simulations are given to show the efficiency of the proposed method.

  • 9.
    Lockby, Andreas
    et al.
    School of Science and Technology, Örebro University, Örebro, Sweden..
    Sandin, Patrik
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems2016In: Comsol Conference 2016, 2016Conference paper (Refereed)
    Abstract [en]

    The dynamical functional particle method(DFPM) is a method for solving equations, e.g. PDEs, using a second order damped dynamical system. We show how the method can be extended to include constraints both explicitly as global constraints and adding the constraints as additional damped dynamical equations. These methods are implemented in Comsol and we show numerical tests for finding the stationary solution of a nonlinear heat equation with and without constraints (global and dynamical). The results show that DFPM is a very general and robust way of solving PDEs and it should be of interest to implement the approach more generally in Comsol.

  • 10.
    Rahayem, Mohamed R.
    et al.
    Örebro University, School of Science and Technology.
    Kjellander, Johan A. P.
    Örebro University, School of Science and Technology.
    Quadric segmentation and fitting of data captured by a laser profile scanner mounted on an industrial robot2010In: The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, E-ISSN 1433-3015, Vol. 52, no 1-4, p. 155-169Article in journal (Refereed)
    Abstract [en]

    Applications like geometric reverse engineering, robot vision and automatic inspection require sets of points to be measured from the surfaces of objects and then processed by segmentation and fitting algorithms to establish shape parameters of interest. In industrial applications where speed, reliability and automatic operation is of interest a measuring system based on a laser profile scanner mounted on an industrial robot can be of interest. In earlier publications we have presented such a system and also a segmentation algorithm for planar surfaces using 2D profile data in combination with robot poses. Due to the data reduction offered by this approach the segmentation algorithm computes faster than algorithms based on 3D point sets alone. Encouraged by the results we have now developed a segmentation algorithm for two different quadric surfaces also based on 2D profiles in combination with robot poses. This paper presents the new algorithm together with test results and also an interesting observation that points to future work.

  • 11.
    Roussou, Alexandra
    et al.
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Smyrnakis, Ioannis
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, Manolis
    Technological Education Institute of Crete, Heraklion, Greece.
    Efremidis, Nikolaos
    Department of Applied Mathematics, University of Crete, Heraklion, Greece.
    Kavoulakis, Georgios
    Technological Education Institute of Crete, Heraklion, Greece.
    Sandin, Patrik
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry2018In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, article id 045006Article in journal (Refereed)
    Abstract [en]

    We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

  • 12.
    Sandin, Patrik
    et al.
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Smyrnakis, J.
    Technological Education Institute of Crete, Heraklion, Greece.
    Magiropoulos, M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Kavoulakis, G. M.
    Technological Education Institute of Crete, Heraklion, Greece.
    Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength2017In: Physical Review E, ISSN 2470-0045, Vol. 95, no 1, article id 012142Article in journal (Refereed)
    Abstract [en]

    Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.

  • 13.
    Sjölander, Arvid
    et al.
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden .
    Lichtenstein, Paul
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden .
    Larsson, Henrik
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden.
    Pawitan, Yudi
    Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden .
    Between-within models for survival analysis.2013In: Statistics in Medicine, ISSN 0277-6715, E-ISSN 1097-0258, Vol. 32, no 18, p. 3067-3076Article in journal (Refereed)
    Abstract [en]

    A popular way to control for confounding in observational studies is to identify clusters of individuals (e.g., twin pairs), such that a large set of potential confounders are constant (shared) within each cluster. By studying the exposure-outcome association within clusters, we are in effect controlling for the whole set of shared confounders. An increasingly popular analysis tool is the between-within (BW) model, which decomposes the exposure-outcome association into a 'within-cluster effect' and a 'between-cluster effect'. BW models are relatively common for nonsurvival outcomes and have been studied in the theoretical literature. Although it is straightforward to use BW models for survival outcomes, this has rarely been carried out in practice, and such models have not been studied in the theoretical literature. In this paper, we propose a gamma BW model for survival outcomes. We compare the properties of this model with the more standard stratified Cox regression model and use the proposed model to analyze data from a twin study of obesity and mortality. We find the following: (i) the gamma BW model often produces a more powerful test of the 'within-cluster effect' than stratified Cox regression; and (ii) the gamma BW model is robust against model misspecification, although there are situations where it could give biased estimates.

  • 14.
    Sørensen, Mads Peter
    et al.
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Falsig Pedersen, Niels
    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    The dynamics of magnetic vortices in type II superconductors with pinning sites studied by the time dependent Ginzburg–Landau model2017In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 533, p. 40-43Article in journal (Refereed)
    Abstract [en]

    We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg–Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by external magnetic fields and external currents. The system is highly nonlinear and the vortices show complex nonlinear dynamical behaviour.

  • 15.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Fornstedt, T.
    aDepartment of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Dai, X.
    School of Computing Science, Zhejiang University City College, Hangzhou, China.
    An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data2017In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985Article in journal (Refereed)
    Abstract [en]

    We present here the theoretical results and numerical analysis of a regularization method for the inverse problem of determining the rate constant distribution from biosensor data. The rate constant distribution method is a modern technique to study binding equilibrium and kinetics for chemical reactions. Finding a rate constant distribution from biosensor data can be described as a multidimensional Fredholm integral equation of the first kind, which is a typical ill-posed problem in the sense of J. Hadamard. By combining regularization theory and the goal-oriented adaptive discretization technique,we develop an Adaptive Interaction Distribution Algorithm (AIDA) for the reconstruction of rate constant distributions. The mesh refinement criteria are proposed based on the a posteriori error estimation of the finite element approximation. The stability of the obtained approximate solution with respect to data noise is proven. Finally, numerical tests for both synthetic and real data are given to show the robustness of the AIDA.

  • 16.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany.
    Gong, Rongfang
    Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China.
    Cheng, Xiaoliang
    Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations2018In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, no 6, article id 065001Article in journal (Refereed)
    Abstract [en]

    This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

  • 17.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology.
    Gulliksson, Mårten
    Örebro University, School of Science and Technology.
    Hernandez Bennetts, Victor
    Örebro University, School of Science and Technology.
    Schaffernicht, Erik
    Örebro University, School of Science and Technology.
    Reconstructing gas distribution maps via an adaptive sparse regularization algorithm2016In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 24, no 7, p. 1186-1204Article in journal (Refereed)
    Abstract [en]

    In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.

  • 18.
    Zhang, Ye
    et al.
    Örebro University, School of Science and Technology.
    Lukyanenko, D. V.
    Physical Faculty, Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia.
    Yagola, A. G.
    Physical Faculty, Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia.
    Using Lagrange principle for solving two-dimensional integral equation with a positive kernel2016In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 24, no 5, p. 811-831Article in journal (Refereed)
    Abstract [en]

    This article is devoted to a Lagrange principle application to an inverse problem of a two-dimensional integral equation of the first kind with a positive kernel. To tackle the ill-posedness of this problem, a new numerical method is developed. The optimal and regularization properties of this method are proved. Moreover, a pseudo-optimal error of the proposed method is considered. The efficiency and applicability of this method are demonstrated in a numerical example of an image deblurring problem with noisy data.

  • 19.
    Ögren, Magnus
    Dept. of Mathematics, Technical University of Denmark, Kongens Lyngby, Denmark.
    ESGI-88 (European Study Group with Industry) workshop on industrial mathematics: Report2012Report (Other academic)
  • 20.
    Ögren, Magnus
    Nano Science Center, Department of Chemistry, University of Copenhagen, Denmark.
    Predicting the Petrophysical Parameters from the Nanoscale Properties of Chalk2013Report (Other academic)
  • 21.
    Ögren, Magnus
    et al.
    Department of Mathematics, Technical University of Denmark, Kgs. Lyngby, Denmark.
    Carlsson, M.
    Center for Mathematical Sciences, Lund University, Lund, Sweden.
    On the dynamics of the Fermi-Bose model2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 1, article id 015005Article in journal (Refereed)
    Abstract [en]

    We consider the exponential matrix representing the dynamics of the Fermi-Bose model in an undepleted bosonic field approximation. A recent application of this model is molecular dimers dissociating into its atomic compounds. The problem is solved in D spatial dimensions by dividing the system matrix into blocks with generalizations of Hankel matrices, here referred to as D-block-Hankel matrices. The method is practically useful for treating large systems, i.e. dense computational grids or higher spatial dimensions, either on a single standard computer or a cluster. In particular the results can be used for studies of three-dimensional physical systems of arbitrary geometry. We illustrate the generality of our approach by giving numerical results for the dynamics of Glauber type atomic pair correlation functions for a non-isotropic three-dimensional harmonically trapped molecular Bose-Einstein condensate.

  • 22.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Physical Sciences, University of Queensland, Brisbane, Australia.
    Atom-atom correlations in colliding Bose-Einstein condensates2009In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 79, no 2, article id 021606Article in journal (Refereed)
    Abstract [en]

    We analyze atom-atom correlations in the s -wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive- P representation and provide analytic insights into the experimental observations of Perrin [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.

  • 23.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Corney, J. F.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    First-principles quantum dynamics for fermions: Application to molecular dissociation2010In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 92, no 3, article id 36003Article in journal (Refereed)
    Abstract [en]

    We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.

  • 24.
    Ögren, Magnus
    et al.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Kheruntsyan, K. V.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Corney, J. F.
    ARC Centre of Excellence for Quantum-Atom Optics, School of Mathematics and Physics, University of Queensland, Brisbane, Australia.
    Stochastic simulations of fermionic dynamics with phase-space representations2011In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 182, no 9, p. 1999-2003Article in journal (Refereed)
    Abstract [en]

    A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains well-bounded, which defines a useful simulation time. We analyse the application of the Gaussian phase-space representation to the dynamics of the dissociation of an ultra-cold molecular gas. We show how the choice of mapping to stochastic differential equations can be used to tailor the stochastic behaviour, and thus the useful simulation time. In the phase-space approach, it is only averages of stochastic trajectories that have a direct physical meaning. Whether particular constants of the motion are satisfied by individual trajectories depends on the choice of mapping, as we show in examples.

1 - 24 of 24
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