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  • 1.
    Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Adaptive computation of aeroacoustic sources for a rudimentary landing gear using lighthill's analogy2011In: 17th AIAA/CEAS AeroacousticsConference 2011: 32nd AIAA Aeroacoustics Conference, 2011Conference paper (Refereed)
    Abstract [en]

    We present our simulation results for the benchmark problem of the ow past a Rudimentary Landing Gear (RLG) using a General Galerkin (G2) nite element method, also referred to as Adaptive DNS/LES. In G2 no explicit subgrid model is used, instead the compuational mesh is adaptively re ned with respect to an a posteriori error es-timate of a quantity of interest in the computation, in this case the drag force on the RLG. Turbulent boundary layers are modeled using a simple wall layer model with the shear stress at walls proportional to the skin friction, which here is assumed to be small and, therefore, can be approximated by zero skin friction. We compare our results with experimental data and other state of the art computations, where we nd good agreement in sound pressure levels, surface velocities and ow separation. We also compare with detailed surface pressure experimental data where we nd largely good agreement, apart from some local dierences for which we discuss possible explanations.

  • 2. Andersson, U
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Ledfelt, G
    Runborg, O
    A contribution to wavelet-based subgrid modeling1999In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 7, no 2, 151-164 p.Article in journal (Refereed)
    Abstract [en]

    A systematic technique for the derivation of subgrid scale models in the numerical solution of partial differential equations is described. The technique is based on Haar wavelet projections of the discrete operator followed by a sparse approximation. As numerical testing suggests, the resulting numerical method will accurately represent subgrid scale phenomena on a coarse grid. Applications to numerical homogenization and wave propagation in materials with subgrid inhomogeneities are presented.

  • 3. Ariel, G.
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). University of Texas at Austin, United States .
    Kreiss, H. -O
    Tsai, R.
    Multiscale computations for highly oscillatory problems2009In: Multiscale Modeling and Simulation in Science, Springer Berlin/Heidelberg, 2009, 237-287 p.Conference paper (Refereed)
    Abstract [en]

    We review a selection of essential techniques for constructing computational multiscale methods for highly oscillatory ODEs. Contrary to the typical approaches that attempt to enlarge the stability region for specialized problems, these lecture notes emphasize how multiscale properties of highly oscillatory systems can be characterized and approximated in a truly multiscale fashion similar to the settings of averaging and homogenization. Essential concepts such as resonance, fast-slow scale interactions, averaging, and techniques for transformations to non-stiff forms are discussed in an elementary manner so that the materials can be easily accessible to beginning graduate students in applied mathematics or computational sciences.

  • 4. Ariel, G.
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Kreiss, H.-O.
    Tsai, R.
    Multiscale computations for highly oscillatory problems, Multiscale Modeling and Simulation in Science2009In: IEEE Computational Science & Engineering, ISSN 1070-9924, E-ISSN 1558-190XArticle in journal (Refereed)
  • 5. Ashyralyev, Allaberen
    et al.
    Arjmand, Doghonay
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Koksal, Muhammet
    Taylor's decomposition on four points for solving third-order linear time-varying systems2009In: Journal of the Franklin Institute, ISSN 0016-0032, E-ISSN 1879-2693, Vol. 346, no 7, 651-662 p.Article in journal (Refereed)
    Abstract [en]

    In the present paper, the use of three-step difference schemes generated by Taylor's decomposition on four points for the numerical solutions of third-order time-varying linear dynamical systems is presented. The method is illustrated for the numerical analysis of an up-converter used in communication systems.

  • 6. Babuska, I.
    et al.
    Nobile, F.
    Tempone, Raul
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 29-32, 2517-2539 p.Article in journal (Refereed)
    Abstract [en]

    This work describes a solution to the validation challenge problem posed at the SANDIA Validation Challenge Workshop, May 21-23, 2006, NM. It presents and applies a general methodology to it. The solution entails several standard steps, namely selecting and fitting several models to the available prior information and then sequentially rejecting those which do not perform satisfactorily in the validation and accreditation experiments. The rejection procedures are based on Bayesian updates, where the prior density is related to the current candidate model and the posterior density is obtained by conditioning on the validation and accreditation experiments. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data.

  • 7. Babuska, I.
    et al.
    Nobile, F.
    Tempone, Raul
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Formulation of the static frame problem2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 29-32, 2496-2499 p.Article in journal (Refereed)
    Abstract [en]

    This report describes a static framework validation challenge problem used in the SANDIA Validation Challenge Workshop, May 21-23, 2006. The challenge problem has clear engineering character, is simple to state and allows many different approaches to solve it. The regulatory assessment problem is to estimate the probability of a given vertical displacement to exceed a prescribed threshold.

  • 8. Babuška, I.
    et al.
    Tempone, Raúl
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Static frame challenge problem: Summary2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, Vol. 197, no 29-32, 2572-2577 p.Article in journal (Refereed)
    Abstract [en]

    This paper summarizes five solutions to the static frame validation challenge problem. The main goal is to highlight the different approaches present at each stage of the solution process. These include, among others, the description of the elastic properties of the frame's material and their calibration, the use of the validation and accreditation experiments for eventual model rejection and the final statement on the desired regulatory compliance, together with its reliability depending on the amount of available experimental data. It is shown that different methodologies lead to significantly different results. Finally, the conclusions highlight the main findings.

  • 9. Bamberberg, A
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Halpern, L
    Joly, P
    Construction and analysis of paraxial approximations in heterogeneous media1986Conference paper (Refereed)
    Abstract [en]

    We design a new family of paraxial equations in heterogeneous medium. For these equations, the reflection-transmission on an interface is continuous, which is not the case for the classical ones.

  • 10. Bamberger, A
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Halpern, L
    Joly, P
    Higher order paraxial wave equation approximations in heterogeneous media1988In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 48, 129-154 p.Article in journal (Refereed)
    Abstract [en]

    A new family of paraxial wave equation approximations is derived. These approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computational problems, e.g., in seismology, underwater acoustics and as artificial boundary conditions. The equations are written as systems which simplify computations. The support and singular support are studied; energy estimates are given which prove the well-posedness. The reflection and transmission are shown to be continuously dependent on material interfaces in heterogeneous media

  • 11. Bamberger, A
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Halpern, L
    Joly, P
    Parabolic wave equation approximations in heterogenous media,1988In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 48, 99-128 p.Article in journal (Refereed)
    Abstract [en]

    The properties of different variants of parabolic approximations of scalar wave equations are analyzed. These equations are of general form which includes those used in seismology, underwater acoustics and other applications. A new version of the parabolic approximation is derived for heterogeneous media. It has optimal properties with respect to wave reflection at material interfaces. The amplitud of the reflected and transmitted waves depend continuously on the interface. Existence, uniqueness and energy estimates are proved.

  • 12.
    Bayer, Christian
    et al.
    Weierstrass Institute for Applied Analysis and Stochastics.
    Hoel, Håkon
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Kadir, Ashraful
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Plechac, Petr
    Dept. of Mathematical Sciences, University of Delaware.
    Sandberg, Mattias
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Szepessy, Anders
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Tempone, Raul
    Division of Mathematics, King Abdullah University of Science and Technology.
    How accurate is molecular dynamics?2012Report (Other academic)
    Abstract [en]

    Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schrödinger equation and stability of the corresponding hitting time Hamilton-Jacobi equation for non ergodic dynamics, bypasses the usual separation of nuclei and electron wave functions, includes caustic states and gives a different perspective on theBorn-Oppenheimer approximation, Schrödinger Hamiltonian systems and numerical simulation in molecular dynamics modeling at constant energy.

  • 13.
    Bayer, Christian
    et al.
    Weierstrass Institute for Applied Analysis and Stochastics.
    Hoel, Håkon
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    von Schwerin, Erik
    King Abdullah University of Science and Technology.
    Tempone, Raul
    King Abdullah University of Science and Technology.
    On non-asymptotic optimal stopping criteria in Monte Carlo simulations2012Report (Other academic)
    Abstract [en]

    We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in numerical examples to perform more reliably and only slightly less efficiently than the second moment based stopping rule.

  • 14.
    Bayer, Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Szepessy, Anders
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Tempone, Raúl
    Adaptive weak approximation of reflected and stopped diffusions2010In: Monte Carlo Methods and Applications, ISSN 1569-3961, Vol. 16, no 1, 1-67 p.Article in journal (Refereed)
    Abstract [en]

    We study the weak approximation problem of diusions, which are reflected at a subset of the boundary of a domain and stopped at the remaining boundary. First, we derive an error representation for the projected Euler method of Costantini, Pacchiarotti and Sartoretto [Costantini et al., SIAM J. Appl. Math., 58(1):73–102, 1998], based on which we introduce two new algorithms. The first one uses a correction term from the representation in order to obtain a higher order of convergence, but the computation of the correction term is, in general, not feasible in dimensions d> 1. The second algorithm is adaptive in the sense of Moon, Szepessy, Tempone and Zouraris [Moon et al., Stoch. Anal. Appl., 23:511–558, 2005], using stochastic refinement of the time grid based on a computable error expansion derived from the representation. Regarding the stopped diusion, it is based in the adaptive algorithm for purely stopped di usions presented in Dzougoutov, Moon, von Schwerin, Szepessy and Tempone [Dzougoutov et al., Lect. Notes Comput. Sci. Eng., 44, 59–88, 2005]. We give numerical examples underlining the theoretical results.

  • 15.
    Brandi, Maya
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Brocke, E
    Talukdar, Husain Ahammad
    KTH, School of Computer Science and Communication (CSC).
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Bhalla, US
    Djurfeldt, Mikael
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Hellgren Kotaleski, Jeanette
    INCF.
    Multiscale modeling through MUSIC multi-simulation: Modeling a dendritic spine using MOOSE and NeuroRD2011In: Front. Neuroinform. Conference Abstract: 4th INCF Congress of Neuroinformatics, 2011Conference paper (Refereed)
    Abstract [en]

    The nervous system encompasses structure and phenomena at different spatial and temporal scales from molecule to behavior. In addition, different scales are described by different physical and mathematical formalisms. The dynamics of second messenger pathways can be formulated as stochastic reaction-diffusion systems [1] while the electrical dynamics of the neuronal membrane is often described by compartment models and the Hodgkin-Huxley formalism. In neuroscience, there is an increasing need and interest to study multi-scale phenomena where multiple scales and physical formalisms are covered by a single model. While there exists simulators/frameworks, such as GENESIS and MOOSE [3], which span such scales (kinetikit/HH-models), most software applications are specialized for a given domain. Here, we report about initial steps towards a framework for multi-scale modeling which builds on the concept of multi-simulations [2]. We aim to provide a standard API and communication framework allowing parallel simulators targeted at different scales and/or different physics to communicate on-line in a cluster environment. Specifically, we show prototype work on simulating the effect on receptor induced cascades on membrane excitability. Electrical properties of a compartment model is simulated in MOOSE, while receptor induced cascades are simulated in NeuroRD  [4,7] . In a prototype system, the two simulators are connected using PyMOOSE [5] and JPype [6]. The two models with their different physical properties (membrane currents in MOOSE, molecular biophysics in NeuroRD), are joined into a single model system.  We demonstrate the interaction of the numerical solvers of two simulators (MOOSE, NeuroRD) targeted at different spatiotemporal scales and different physics while solving a multi-scale problem. We analyze some of the problems that may arise in multi-scale multi-simulations and present requirements for a generic API for parallel solvers. This work represents initial steps towards a flexible modular framework for simulation of large-scale multi-scale multi-physics problems in neuroscience. References 1. Blackwell KT: An efficient stochastic diffusion algorithm for modeling second messengers in dendrites and spines. J Neurosci Meth 2006, 157: 142-153. 2. Djurfeldt M, Hjorth J, Eppler JM, Dudani N, Helias M, Potjans TC, Bhalla US, Diesmann M, Hellgren Kotaleski J, Ekeberg Ö: Run-Time Interoperability Between Neural Network Simulators Based on the MUSIC Framework. Neurinform 2010, 8: 43-60. 3. Dudani N, Ray S, George S, Bhalla US: Multiscale modeling and interoperability in MOOSE. Neuroscience 2009, 10(Suppl 1): 54. 4. Oliveira RF, Terrin A, Di Benedetto G, Cannon RC, Koh W, Kim M, Zaccolo M, Blacwell KT: The Role of Type 4 Phosphdiesterases in Generating Microdomains of cAMP: Large Scale Stochastic Simulations.

  • 16.
    Brandi, Maya
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB. KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Brocke, Ekaterina
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Talukdar, Husain A.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Bhalla, Upinder S.
    National Centre for Biological Sciences, Bangalore, India.
    Hällgren-Kotaleski, Jeanette
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Djurfeldt, Mikael
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC.
    Connecting MOOSE and NeuroRD through MUSIC: towards a communication framework for multi-scale modeling2011In: Twentieth Annual Computational Neuroscience Meeting: CNS*2011, Springer Science+Business Media B.V., 2011Conference paper (Refereed)
  • 17. Brenan, K.E.
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Backward differentiation approximations of nonlinear differential/algebraic systems1988In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 51, no 84, 659-676 p.Article in journal (Refereed)
    Abstract [en]

    Finite-difference approximations of dynamical systems modeled by nonlinear, semiexplicit, differential/algebraic equations are analyzed. Convergence for the backward differentiation method is proved for index two and index three problems when the numerical initial values obey certain constraints. The appropriate asymptotic convergence rates and the leading error terms are determined.

  • 18.
    Carlsson, Jesper
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Sandberg, Mattias
    Univ Oslo, CMA.
    Szepessy, Anders
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Symplectic Pontryagin Approximations for Optimal Design2009In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 43, no 1, 3-32 p.Article in journal (Refereed)
    Abstract [en]

    The powerful Hamilton-Jacobi theory is used for constructing regularizations and error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method for optimal design and reconstruction: the first, analytical, step is to regularize the Hamiltonian; next the solution to its stationary Hamiltonian system, a nonlinear partial differential equation, is computed with the Newton method. The method is efficient for designs where the Hamiltonian function can be explicitly formulated and when the Jacobian is sparse, but becomes impractical otherwise (e.g. for non local control constraints). An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its L 2 projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems.

  • 19.
    Chaudhry, Qasim Ali
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    PAHs are the reactive toxic chemical compounds which are present as environmental pollutants. These reactive compounds not only diffuse through the membranes of the cell but also partition into the membranes. They react with the DNA of the cell giving rise to toxicity and may cause cancer. To understand the cellular behavior of these foreign compounds, a mathematical model including the reaction-diffusion system and partitioning phenomenon has been developed. In order to reduce the complex structure of the cytoplasm due to the presence of many thin membranes, and to make the model less computationally expensive and numerically treatable, homogenization techniques have been used. The resulting complex system of PDEs generated from the model is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. Then the model was reduced to a system of ODEs, a compartment model (CM). The quantitative analysis of the results of the CM shows that it cannot fully capture the features of metabolic system considered in general. Thus the PDE model affords a more realistic representation. In order to see the influence of cell geometry in drug diffusion, the non-spherical axi-symmetric cell geometry is considered, where we showed that the cellular geometry plays an important role in diffusion through the membranes. For further reduction of complexity of the model, another simplified model was developed. In the simplified model, we used PDEs for the extracellular domain, cytoplasm and nucleus, whereas the plasma and nuclear membranes were taken away, and replaced by the membrane flux, using Fick's Law. We further extended the framework of our previously developed model by benchmarking against the results from four different cell lines. Global optimization techniques are used for the parameters describing the diffusion and reaction to fit the measured data. Numerical results were in good agreement with the in vitro results. For the further development of the model, the process of surface bound reactions were added, thus developing a new cell model. The effective equations were derived using iterative homogenization for this model. The numerical results of some of the species were qualitatively verified against the in vitro results found in literature.

  • 20.
    Chaudhry, Qasim Ali
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Numerical Approximation of Reaction and Diffusion Systems in Complex Cell Geometry2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model.

  • 21.
    Chaudhry, Qasim Ali
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Dreij, Kristian
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Morgenstern, Ralf
    Numerical Approximation of Reaction and Diffusion Systems in Mammalian Cell Using Homogenization and Compartment Modelling2010Conference paper (Refereed)
  • 22.
    Chaudhry, Qasim Ali
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Dreij, Kristian
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Morgenstern, Ralf
    Spatially Distributed Models Instead of Compartment Models are Necessary for Accurate Capture of the Intracellular Dynamics of Lipophilic Compounds2010Conference paper (Refereed)
  • 23.
    Chaudhry, Qasim Ali
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Dreij, Kristian
    Morgenstern, Ralf
    Mathematical Modeling of Reaction and Diffusion Systems in a Cell Including Surface Reactions on the Cytoplasmic Membranes2012Report (Other academic)
    Abstract [en]

    Benzo[a]pyrene (BP) is a toxic polycyclic aromatic hydrocarbon (PAH) whichis found in our environment. These BPs are metabolized to benzo[a]pyrene diol(BPD) by enzymes bound to the cytoplasmic membranes e.g. members of thecytochrome P450 protein family and epoxide hydrolyses. BPDs are further metabolizedto two stereochemical variants of Benzo[a]pyrene diol expoxide (BPDE) bythe cytochrome P450 family of proteins. These are the two steps of metabolismcategorized as Phase I. In Phase II, BPDEs are further metabolized by soluble enzymesin the cytoplasm e.g. members of the glutathione transferase protein familyto GSH conjugates. BPDE can also diffuse into the cellular nucleus and reactwith DNA forming mutagenic DNA adducts. The formation of GSH conjugatesand DNA adducts, was earlier studied by us by developing a mathematical modeldescribing the intracellular reaction and diffusion of lipophilic PAHs taking intoaccount the partitioning phenomenon (Dreij K et al. PLoS One 6(8), 2011). In thispaper part of Phase I metabolism i.e formation of BPDE metabolites, will be addedto the model, thus enhancing the previous model. These cytochrome P450 reactionstake place on the intracellular membranes, and are modeled as a membranesurface reaction within the cytoplasm using the standard process of adsorption anddesorption. The effective equations are derived using iterative homogenization forthe numerical treatment of the cytoplasm including surface effects. The numericalresults of some of the species have been qualitatively verified against in vitroresults found in the literature.

  • 24.
    Chaudhry, Qasim Ali
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Morgenstern, Ralf
    Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
    On the numerical approximation of drug diffusion in complex cell geometry2009In: Proceedings of the 6th International Conference on Frontiers of Information Technology, FIT '09, Abbottabad, 2009Conference paper (Other academic)
    Abstract [en]

    The mathematical modeling of a mammalian cell is a very tedious work due to its very complex geometry. Especially, taking into account the spatial distribution and the inclusion of lipophilic toxic compounds greatly increases its complexity. The nonhomogeneity and the different cellular architecture of the cell certainly affect the diffusion of these compounds. The complexity of the whole system can be reduced by a homogenization technique. To see the effect of these compounds on different cell architectures, we have implemented a mathematical model. The work has been done in 2-dimensional space. The simulation results have been qualitatively verified using compartmental modeling approach. This work can be extended with a more complex reaction-diffusion system and to 3-dimensional space as well. Copyright 2009 ACM.

  • 25.
    Chaudhry, Qasim Ali
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Morgenstern, Ralf
    Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
    Simulation of transport of lipophilic compounds in complex cell geometry2009In: Proceedings of the COMSOL Conference, Milan, 2009, 2009Conference paper (Refereed)
  • 26.
    Chaudhry, Qasim Ali
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Morgenstern, Ralf
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Dreij, Kristian
    Influence of Biological Cell Geometry on Reaction and Diffusion Simulation2012Report (Other academic)
    Abstract [en]

    Mathematical modeling of reaction-diffusion system in a biological cellis an important and difficult task, especially when the chemical compoundsare lipophilic. The difficulty level increases, when we take into account theheterogeneity of the cell, and the variation of cellular architecture. Mathematicalmodeling of reaction-diffusion systems in spherical cell geometryhas earlier been performed by us. In the present paper, we have workedwith non-spherical cell geometry, because the cellular geometry can play animportant role for drug diffusion in the cell. Homogenization techniques,which were earlier applied in the case of a spherical cell model, have beenused for the numerical treatment of the model. This technique considerablyreduces the complexity of the model. To further reduce the complexity ofthe model, a simplified model was also developed. The key idea of this simplifiedmodel has been advocated in Virtual Cell, where PDEs are used forthe extracellular domain, cytoplasm and nucleus, whereas the plasma andnuclear membranes have been taken away, and replaced by membrane flux,using Fick’s Law of diffusion. The numerical results of the non-sphericalcell model have been compared with the results of the spherical cell model,where the numerical results of spherical cell model have already been validatedagainst in vitro cell experimental results. From the numerical results,we conclude that the plasma and nuclear membranes can be protective reservoirsof significance. The numerical results of the simplified model werecompared against the numerical results of our detailed model, revealing theimportance of detailed modeling of membranes in our model.

  • 27.
    Christensen, Henrik I.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Session summary2005In: Robotics Research: The Eleventh International Symposium, Springer Berlin/Heidelberg, 2005, 57-59 p.Chapter in book (Refereed)
    Abstract [en]

    While the current part carries the title “path planning” the contributions in this section cover two topics: mapping and planning. In some sense one might argue that intelligent (autonomous) mapping actually requires path planning. While this is correct the contributions actually have a broader scope as is outlined below. A common theme to all of the presentations in this section is the adoption of hybrid representations to facilitate efficient processing in complex environments. Purely geometric models allow for accurate estimation of position and motion generation, but they scale poorly with environmental complexity while qualitative geometric models have a limited accuracy and are well suited for global estimation of trajectories/locations. Through fusion of qualitative and quantitative models it becomes possible to develop systems that have tractable complexity while maintaining geometric accuracy.

  • 28. Clayton, R
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Absorbing boundary conditions for acoustic and elastic wave equations1977In: Bulletin of The Seismological Society of America (BSSA), ISSN 0037-1106, E-ISSN 1943-3573, Vol. 67, no 6, 1529-1540 p.Article in journal (Refereed)
    Abstract [en]

    The two dimensional elastic wave equations are used to model wave propagation in mediums with large or unbounded domains. In order to numerically simulate those problems the equations have to be put on the computer and artificial boundary conditions that allow minimal wave reflection must be introduced. These boundary conditions are well known in the literature as absorbing or radiating boundary conditions. They have been of interest to physicists and meteorologists for some time. In this paper three different methods for deriving radiating boundary conditions for the elastic wave equations are presented. One of these techniques gives exact absorbing boundary conditions for both P (longitudinal) and S (transverse) waves generated from a surface source. From this, approximate absorbing boundary conditions are derived. These conditions are easy to employ in finite difference codes.

  • 29. Clayton, R.W.
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Absorbing boundary conditions for wave-equation migration1980In: Geophysics, ISSN 0016-8033, E-ISSN 1942-2156, Vol. 45, no 5, 895-904 p.Article in journal (Refereed)
    Abstract [en]

    The standard boundary conditions used at the sides of’s seismic section in wave-equation migration generateartificial reflections. These reflections from the edges of the computational grid appear as artifacts in the finalsection. Padding the section with zero traces on either 5ide adds to the cost of’migration and simply delays theine\ itable reflections.We develop stable absorbing boundary condition5 that annihilate almost all of the artificial reflections. Thisih demonstrated analytically and with synthetic examples. The absorbing boundary conditions presented canbe used with any ofthe different type\ of finite-diftcrence wa\e-equation migration, at essentially no extra cost.

  • 30. Compere, Gaetan
    et al.
    Remacle, Jean-Francois
    Jansson, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A mesh adaptation framework for dealing with large deforming meshes2010In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 82, no 7, 843-867 p.Article in journal (Refereed)
    Abstract [en]

    In this paper. we identify and propose solutions for several issues encountered when designing a mesh adaptation package, such as mesh-to-mesh projections and mesh database design, and we describe an algorithm to integrate a mesh adaptation procedure in a physics solver. The open-source MAdLib package is presented as an example of such a mesh adaptation library. A new technique combining global node repositioning and mesh optimization in order to perform arbitrarily large deformations is also proposed. We then present several test cases to evaluate the performances of the proposed techniques and to show their applicability to fluid-structure interaction problems with arbitrarily large deformations. Copyright (C) 2009 John Wiley & Sons, Ltd.

  • 31.
    Da Ronch, A.
    et al.
    Department of Engineering, University of Liverpool, UK.
    McFarlane, C.
    Department of Aerospace Engineering, Bristol University, UK.
    Oppelstrup, Jesper
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Zhang, Mengmeng
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Aerodynamics.
    Rizzi, Arthur
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Aerodynamics.
    Benchmarking CEASIO software to predict flight control and flying qualities of the B-7472010In: 27th International Congress of the Aeronautical Sciences, ICAS 2010, 2010Conference paper (Refereed)
  • 32. Davoli, Paolo
    et al.
    Monari, Matteo
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Severinsson Eklundh, Kerstin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Peer activities on Web learning platforms: Impact on collaborative writing and usability issues2009In: Education and Information Technologies: Official Journal of the IFIP technical committee on Education, ISSN 1360-2357, E-ISSN 1573-7608, Vol. 14, no 3, 229-254 p.Article in journal (Refereed)
    Abstract [en]

    The importance of groupware tools in e-learning practice is increasing, because of their educational relevance and of the importance of group abilities in today's job activities. The paper addresses some critical issues of asynchronous collaborative tools hosted in Web-learning platforms. A model to capture user quality perceptions for these tools is presented, and an investigation conducted in three case studies where e-learning platforms were used to share and comment on written works is reported in detail. Quantitative and qualitative data are used in a complementary way to capture the complexity of educational collaborative activities. The impact of technologies on work organization, writing and peer-feedback activities is discussed. Users dedicated more time to feedback activities than they would have in real-life contexts, and paid more attention to the style and content of their writing. Communication was more focused and honest than in real life (even though more distant and at the risk of misunderstanding), and its indirectness encouraged shy and impaired people. Usability problems emerged from platform design, educators' choices and server-side settings; Web-based systems seem to pose specific usability issues when users are required a strong active role; compatibility issues highlight the need for a closer Web standard compliance.

  • 33.
    de Abreu, Rodrigo Vilela
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Adaptive Computation of Aeroacoustic Sources for Rudimentary Landing Gear2010In: Benchmark problems for Airframe Noise Computations I, Stockholm 2010, 2010Conference paper (Other academic)
  • 34. Deuflhard, P
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Large scale scientific computing: Proceedings of workshop held at the Oberwolfach Mathematical Institute1987 (ed. 7)Book (Refereed)
    Abstract [en]

    The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research and teaching - quickly, informally, and at a high level.

    The cornerstone of LNCS's editorial policy is its unwavering commitment to report the latest results from all areas of computer science and information technology research, development, and education. LNCS has always enjoyed close cooperation with the computer science R & D community, with numerous renowned academics, and with prestigious institutes and learned societies. Our mission is to serve this community by providing a most valuable publication service.

    LNCS commenced publication in 1973 and quite rapidly attracted attention, not least because of its thus far unprecedented publication turnaround times. The 1980s and 1990s witnessed a substantial growth in the series, particularly in terms of volumes published. In the late 1990s we developed a systematic approach to providing LNCS in a full-text electronic version, in parallel to the printed books. Another new feature introduced in the late 1990s was the conceptualization of a couple of color-cover sublines. Still, original research results reported in proceedings and postproceedings remain the core of LNCS.

  • 35. Diehl, Moritz
    et al.
    Glineur, FrançoisJarlebring, EliasKTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).Michiels, Wim
    Recent Advances in Optimization and its Applications in Engineering2010Collection (editor) (Refereed)
    Abstract [en]

    Mathematical optimization encompasses both a rich and rapidly evolving body of fundamental theory, and a variety of exciting applications in science and engineering. The present book contains a careful selection of articles on recent advances in optimization theory, numerical methods, and their applications in engineering. It features in particular new methods and applications in the fields of optimal control, PDE-constrained optimization, nonlinear optimization, and convex optimization. The authors of this volume took part in the 14th Belgian-French-German Conference on Optimization (BFG09) organized in Leuven, Belgium, on September 14-18, 2009. The volume contains a selection of reviewed articles contributed by the conference speakers as well as three survey articles by plenary speakers and two papers authored by the winners of the best talk and best poster prizes awarded at BFG09. Researchers and graduate students in applied mathematics, computer science, and many branches of engineering will find in this book an interesting and useful collection of recent ideas on the methods and applications of optimization.

  • 36. Dorobantu, M
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Wavelet-based numerical homogenization1998In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 35, no 2, 540-559 p.Article in journal (Refereed)
    Abstract [en]

    A numerical homogenization procedure for elliptic differential equations is presented. It is based on wavelet decompositions of discrete operators in find and coarse scale components followed by the elemination of the fine scale contributions. If the operator is in divergence form, this is preserved by the homogenization procedure. For periodic problems, results similar to classical effective coefficient theory is proved. The procedure can be applied to problems that are not cell-periodic.

  • 37.
    Dreij, Kristian
    et al.
    Karolinska Inst, Stockholm, Sweden .
    Chaudhry, Qasim A.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Zhang, Jie
    Karolinska Inst, Stockholm, Sweden .
    Sundberg, Kathrin
    Karolinska Inst, Stockholm, Sweden .
    Jernström, Bengt
    Karolinska Inst, Stockholm, Sweden .
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Morgenstern, Ralf
    Karolinska Inst, Stockholm, Sweden .
    In silico modeling of the intracellular dynamics of polycyclic aromatic hydrocarbons2012In: Toxicology Letters, ISSN 0378-4274, E-ISSN 1879-3169, Vol. 211, S60-S61 p.Article in journal (Other academic)
  • 38. Dreij, Kristian
    et al.
    Chaudhry, Qasim Ali
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Jernstrom, Bengt
    Morgenstern, Ralf
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    A Method for Efficient Calculation of Diffusion and Reactions of Lipophilic Compounds in Complex Cell Geometry2011In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 6, no 8, e23128- p.Article in journal (Refereed)
    Abstract [en]

    A general description of effects of toxic compounds in mammalian cells is facing several problems. Firstly, most toxic compounds are hydrophobic and partition phenomena strongly influence their behaviour. Secondly, cells display considerable heterogeneity regarding the presence, activity and distribution of enzymes participating in the metabolism of foreign compounds i.e. bioactivation/biotransformation. Thirdly, cellular architecture varies greatly. Taken together, complexity at several levels has to be addressed to arrive at efficient in silico modelling based on physicochemical properties, metabolic preferences and cell characteristics. In order to understand the cellular behaviour of toxic foreign compounds we have developed a mathematical model that addresses these issues. In order to make the system numerically treatable, methods motivated by homogenization techniques have been applied. These tools reduce the complexity of mathematical models of cell dynamics considerably thus allowing to solve efficiently the partial differential equations in the model numerically on a personal computer. Compared to a compartment model with well-stirred compartments, our model affords a more realistic representation. Numerical results concerning metabolism and chemical solvolysis of a polycyclic aromatic hydrocarbon carcinogen show good agreement with results from measurements in V79 cell culture. The model can easily be extended and refined to include more reactants, and/or more complex reaction chains, enzyme distribution etc, and is therefore suitable for modelling cellular metabolism involving membrane partitioning also at higher levels of complexity.

  • 39. Dreij, Kristian
    et al.
    Chaudhry, Qasim Ali
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Jernström, Bengt
    Hanke, Michael
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Morgenstern, Ralf
    In silico Modeling of Intracellular Diffusion and Reaction of Benzo[a]pyrene Diol Epoxide2012Report (Other academic)
    Abstract [en]

    Several studies has suggested that glutathione conjugation of polycyclicaromatic hydrocarbons (PAHs) catalyzed by glutathione transferases (GSTs)are important factors in protecting cells against toxicity and DNA damagederived from these compounds. To further characterize the intracellular dynamicsof PAH DEs and the role of GSTs in protection against DNA damage,we recently developed a PDE model using techniques for mathematicalhomogenization (Dreij K et al. PLoS One 6(8), 2011). In this study, wewanted to further develop our model by benchmarking against results fromfour V79 cell lines; control cells and cells overexpressing human GSTs A1-1, M1-1 and P1-1. We used an approach of global optimization of the parametersdescribing the diffusion and reaction of the ultimate carcinogenic PAHmetabolite benzo[a]pyrene diol epoxide to fit measured values from the fourV79 cell lines. Numerical results concerning the formation of glutathioneconjugates and hydrolysis were in good agreement with results from measurementsin V79 cell culture. Cellular results showed significant protectionby GST expression against formation of DNA adducts with more than 10-fold reduced levels compared to control cells. Results from the model usingglobally optimized parameters showed that the model cannot predict theprotective effects of GSTs. Extending the model to also include effects fromprotein interactions and GST localization showed the same discrepancy. Insummary, the results show that we have an incomplete understanding of theintracellular dynamics of the interaction between BPDE and GST that warrantsfurther investigation and development of the model.

  • 40.
    Dubus, Gaël
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Convergence improvement and qualification of a model for fission gas behaviour in nuclear fuel2007Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    During the irradiation in a fuel assembly of a Pressurized Water Reactor (PWR), the thermal diffusion processes are not the only active mechanisms: the effects of irradiation are significant, involving variations of the diffusion coefficients as well as creation and evolution of point defects and cavities in the material.In this document we present the work we have done on MOGADOR, a numerical fission gas behaviour model for nuclear fuel under irradiation in a PWR focusing on the modelling of the behaviour of irradiation defects, fission gases and as-fabricated pores. This work has been accomplished within the frame of a six-month internship, from September 2006 to March 2007 at the LSC laboratory, located at the Cadarache research centre.The first task was to optimize the model and to improve its convergence in a simplified case, which was a necessary condition to go further with the study of a complete case. Then we started to tackle the physical qualification of MOGADOR, that is to say verify the behaviour of some physical quantities and their dependencies to some parameters. We present also a short review of numerical methods commonly used for solving ordinary differential equations.

  • 41. Durlofsky, L. J.
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Osher, S
    Triangle based adaptive stencils for the solution of hyperbolic conservation laws1992In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, ISSN 0021-9991, Vol. 98, no 1, 64-73 p.Article in journal (Refereed)
    Abstract [en]

    A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

  • 42. Edstrom, Per
    et al.
    Neuman, Magnus
    Avramidis, Stefanos
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Andersson, Mattias
    Geometry Related Inter-Instrument Differences in Spectrophotometric Measurements2010In: Nordic Pulp & Paper Research Journal, ISSN 0283-2631, E-ISSN 2000-0669, Vol. 25, no 2, 221-232 p.Article in journal (Refereed)
    Abstract [en]

    The L&W Elrepho d/0 and the Spectrolino 45/0 instruments are examined using paper samples with different properties. External factors that influence the measurements such as the sample background, the instrument calibration and the sample inhomogeneity are studied, and a methodology for their minimization is presented. Experimental measurements show that such external factors, if not minimized by proper routines, affect the inter-instrument differences far more (up to 4-5 Delta E-ab(star)) than the instrument geometry (the effect of which is small and of order 0.1 Delta E-ab(star)). The DORT2002 radiative transfer model is used to simulate differences caused by instrument geometry. The simulated and measured differences are found to agree in magnitude, and the differences are mapped against sample properties. It is observed that the 45/0 instrument detects higher reflectance from paper samples with negligible absorption and transmittance. When there is considerable absorption (dyed samples) or transmittance (thin samples), the d/0 instrument detects higher reflectance. The physical mechanism behind this behavior is studied and explained using DORT2002, and the instrument differences are shown to depend on the anisotropy of the reflected light. The model/measurement agreement is satisfactory as the characteristic behavior is captured in almost all cases studied. This new understanding is important for facilitating accurate data exchange between the paper and graphic arts industries, but also for interpretation of reflectance measurements in general.

  • 43.
    Elenius, Måns
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Dzugutov, Mikhail
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Evidence for a liquid-solid critical point in a simple monatomic system2009In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 131, no 10, 104502- p.Article in journal (Refereed)
    Abstract [en]

    It is commonly believed that the transition line separating a liquid and a solid cannot be interrupted by a critical point. This opinion is based on the traditional symmetry argument that an isotropic liquid cannot be continuously transformed into a crystal with a discrete rotational and translational symmetry. We present here a molecular-dynamics simulation of a simple monatomic system suggesting the existence of a liquid-solid spinodal terminating at a critical point. We show that, in the critical region, the isotropic liquid continuously transforms into a phase with a mesoscopic order similar to that of the smectic liquid crystals. We argue that the existence of both the spinodal and the critical point can be explained by the close structural proximity between the mesophase and the crystal. This indicates a possibility of finding a similar thermodynamic behavior in gelating colloids, liquid crystals, and polymers.

  • 44.
    Elenius, Måns
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Oppelstrup, Tomas
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Dzugutov, Mikhail
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Evidence for a simple monatomic ideal glass former: The thermodynamic glass transition from a stable liquid phase2010In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 133, no 17, 174502- p.Article in journal (Refereed)
    Abstract [en]

    Under cooling, a liquid can undergo a transition to the glassy state either as a result of a continuous slowing down or by a first-order polyamorphous phase transition. The second scenario has so far always been observed in a metastable liquid domain below the melting point where crystalline nucleation interfered with the glass formation. We report the first observation of the liquid-glass transition by a first-order polyamorphous phase transition from the equilibrium stable liquid phase. The observation was made in a molecular dynamics simulation of a one-component system with a model metallic pair potential. In this way, the model, demonstrating the thermodynamic glass transition from a stable liquid phase, may be regarded as a candidate for a simple monatomic ideal glass former. This observation is of conceptual importance in the context of continuing attempts to resolve the long-standing Kauzmann paradox. The possibility of a thermodynamic glass transition from an equilibrium melt in a metallic system also indicates a new strategy for the development of bulk metallic glass-forming alloys.

  • 45. Eliasson, P
    et al.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    The effect of dissipation and coarse grid resolution for multigrid in flow problem1996Conference paper (Refereed)
    Abstract [en]

    This paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For twodimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density

  • 46.
    Engblom, Stefan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    On well-separated sets and fast multipole methods2011In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 61, no 10, 1096-1102 p.Article in journal (Refereed)
    Abstract [en]

    The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more liberal than in conventional codes. Such variants offer a particularly elegant implementation with a balanced multipole tree, a feature which might be very favorable on modern computer architectures.

  • 47.
    Engblom, Stefan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    PARALLEL IN TIME SIMULATION OF MULTISCALE STOCHASTIC CHEMICAL KINETICS2009In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 8, no 1, 46-68 p.Article in journal (Refereed)
    Abstract [en]

    A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate equation. A stochastic simulation algorithm is used to obtain an exact realization of the process at the mesoscopic scale (in parallel). The underlying stochastic description is a jump process driven by the Poisson measure. A convergence result in this arguably difficult setting is established, suggesting that a homogenization of the solution is advantageous. We devise a simple but highly general such technique. Three numerical experiments on models representative to the field of computational systems biology illustrate the method. For nonstiff problems, it is shown that the method is able to quickly converge even when stochastic effects are present. For stiff problems, we are instead able to obtain fast convergence to a homogenized solution. Overall, the method builds an attractive bridge between, on the one hand, macroscopic deterministic scales and, on the other hand, mesoscopic stochastic ones. This construction is clearly possible to apply also to stochastic models within other fields.

  • 48.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Far field computational boundary conditions1989In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 7, no 2, 113-120 p.Article in journal (Refereed)
  • 49.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Inverse imaging methods in exploration seismology1980Conference paper (Refereed)
  • 50.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Numerical computation of oscillatory solutions to hyperbolic problems1991Conference paper (Refereed)
123456 1 - 50 of 295
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