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  • 101.
    Polyakov, Eugeniy
    et al.
    Stockholm University, Faculty of Science, Department of Physical, Inorganic and Structural Chemistry.
    Vorontsov-Velyaminov, Pavel
    St.Petersburg State University.
    Lyubartsev, Alexander
    Stockholm University, Faculty of Science, Department of Physical, Inorganic and Structural Chemistry.
    Stochastic positive P-representation in problems of quantum statistics. Simulation of one-dimensional Bose-gas with delta-repulsion2009In: Vychislitel'nye Metody i Programirovaniye [Numerical methods and programming], ISSN 0507-5386, Vol. 10, p. 223-247Article in journal (Other academic)
    Abstract [en]

    A method of stochastic positive P-representation for the computer simulation of thermal equilibrium and dynamical properties of many-particle quantum systems with interactions is proposed and thoroughly analyzed. The testing procedure of the method includes the evaluation of spatial correlation functions for the one-dimensional Bose-gas with delta-repulsion between particles, both in the state of thermal equilibrium and in the dynamical evolution from a given initial state. This work was supported by the Russian Foundation for Basic Research (project number 08–02–00041) and by the Royal Swedish Academy of Sciences.

     

  • 102.
    Rosquist, Kjell
    Stockholm University, Faculty of Science, Department of Physics.
    A dielectric analogue model of the Kerr equatorial plane2008In: Proceedings of the eleventh Marcel Grossmann meeting: On recent developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, 2008, p. 1475-1478Conference paper (Refereed)
    Abstract [en]

    An optical analogue solution of the Kerr equatorial plane is given. To find the solution a special notation for calculations with two different metrics has been used. The possibility of extending the solution to the complete Kerr geometry is also discussed.

  • 103.
    Rosquist, Kjell
    Stockholm University, Faculty of Science, Department of Physics.
    A link between general relativity and quantum mechanics2008In: The eleventh Marcel Grossmann meeting: On recent developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, 2008, p. 2634-2638Conference paper (Refereed)
    Abstract [en]

    For a number of reasons including having a Dirac g-factor g = 2, the most probable approximation for the exterior gravitational and electromagnetic field of the electron is the Kerr-Newman solution to the Einstein-Maxwell equations. It is shown that the Kerr-Newman solution when used as the exterior Einstein-Maxwell field for the electron gives rise to a standard statistical measuring uncertainty in the position of the particle. The size of the uncertainty is the Compton wavelength. The uncertainty therefore coincides with that which is usually inferred for the electron in the context of relativistic quantum mechanics.

  • 104.
    Rosquist, Kjell
    Stockholm University, Faculty of Science, Department of Physics.
    A unifying coordinate family for the Kerr-Newman metric2009In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 41, p. 2619-2632Article in journal (Refereed)
    Abstract [en]

    A new unified metric form is presented for the Kerr–Newman geometry. The new form is a generalization of the Boyer–Lindquist metric involving an arbitrary gauge function of the spheroidal radial variable. Each choice of the gauge function corresponds to a coordinate system including four of the most important coordinate systems for Kerr–Newman (Boyer–Lindquist, Kerr, Kerr–Schild and Doran coordinates). The representation is given in terms of a single Minkowski frame together with the gauge function. This Minkowski frame arises by boosting a static orthonormal frame which is adapted to spheroidal coordinates. Properties of the boost reflect the rotating nature of the Kerr–Newman solution including an identification of the angular velocities of the disk and the horizon matching previously known values obtained in other ways.

  • 105.
    Rosquist, Kjell
    Stockholm University, Faculty of Science, Department of Physics.
    Some Consequences of Gravitationally Induced Electromagnetic Fields in Microphysics2010In: Journal of the Korean Physical Society, ISSN 0374-4884, E-ISSN 1976-8524, Vol. 56, no 5 (Pt. I), p. 1612-1618Article in journal (Refereed)
    Abstract [en]

    We discuss the relation between the gravitational and electromagnetic fields as governed by the Einstein-Maxwell field equations. It is emphasized that the tendency of the gravitational field to induce electromagnetic effects increases as the size of the system decreases. This is because the charge-to-mass ratio $Q/M$ is typically larger in smaller systems. For most astrophysical systems, $Q/M$ is $\ll 1$ while for a Millikan oil drop, $Q/M \sim 10^6$. Going all the way down to elementary particles, the value for the electron is $Q/M \sim 10^{21}$. For subatomic systems there is an additional phenomenon which comes into play. In fact, according to general relativity, the gravitational field tends to become dominated by the spin at distances of the order of the Compton wavelength.The relevant quantity which governs this behavior is the ratio $S/M^2$ where $S$ is the (spin) angular momentum. For an electron, $S/M^2 \sim 10^{44}$.As a consequence, the gravitational field becomes dominated by gravitomagnetic effects in the subatomic domain.This fact has important consequences for the electromagnetic fields of spinning charged particles.To analyze this situation we use the asymptotic structure in the form of the multipole fields.%Such an approach avoids the pitfalls should one try to use a near-field approach using some kind of semi-classical formulation of the Einstein-Maxwell equations for example. To obtain more exact results however, one must take quantum effects into account including radiative contributions. Although such effects are not considered in this work, the order of magnitude of the considered effects are not expected to change drastically when going to a quantum mechanical treatment. The most relevant solution of the Einstein-Maxwell equations in this context is the Kerr-Newman metric. It is the preferred solution which is in accord with all the four known multipole moments of the electron to an accuracy of one part in a thousand. Our main result is that general relativity predicts corrections to the Coulomb field for charged spinning sources. Experimentally verifiable consequences include a predicted electric quadrupole moment for the electron, possible quasi-bound states in positron-heavy ion scattering with sizes corresponding to observed anomalous peaks, as well as small corrections to energy levels in microscopic bound systems such as the hydrogen atom

  • 106.
    Rosquist, Kjell
    Stockholm University, Faculty of Science, Department of Physics.
    Some physical consequences of the multipole structure of the Kerr and Kerr-Newman solutions2008In: The eleventh Marcel Grossmann meeting: On recent developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, 2008, p. 2294-2298Conference paper (Refereed)
    Abstract [en]

    We discuss physical aspects of the Kerr and Kerr-Newman solutions relating to the multipole structure, especially its nonlinear nature in general relativity. It is argued that the Kerr and Kerr-Newman multipole structure is likely to be important for general macroscopic as well as microscopic systems.

  • 107.
    Rosquist, Kjell
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bylund, Tomas
    Stockholm University, Faculty of Science, Department of Physics.
    Samuelsson, Lars
    Nordita.
    Carter's constant revealed2009In: International Journal of Modern Physics D, ISSN 0218-2718, Vol. 18, no 3, p. 429-434Article in journal (Refereed)
  • 108.
    Saelen, Lene
    et al.
    Department of physics and technology, University of Bergen, Norway.
    Waltersson, Erik
    Stockholm University, Faculty of Science, Department of Physics.
    Hansen, J. P.
    Department of physics and technology, University of Bergen, Norway.
    Lindroth, Eva
    Stockholm University, Faculty of Science, Department of Physics.
    Fundamental gates for a strongly correlated two-electron quantum ring2010In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 81, no 3, p. 033303-Article in journal (Refereed)
    Abstract [en]

    We demonstrate that conditional as well as unconditional basic operations which are necessary for universal quantum gates can be performed with almost 100% fidelity within a strongly interacting two-electron quantum ring. Both sets of operations are based on a quantum control algorithm that optimizes a driving electromagnetic pulse for a given quantum gate. The demonstrated transitions occur on a time scale much shorter than typical decoherence times of the system.

  • 109.
    Sandström, Helena
    Stockholm University, Faculty of Science, Department of Physics.
    Contouring & planning variability in stereotactic radiosurgery: How to assess and address the weakest link in stereotactic radiosurgery?2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The use of stereotactic radiosurgery (SRS) employing one or a few fractions of high doses of radiation has continuously increased due to the technical development in dose delivery and morphological and functional imaging. As the target volume in SRS is usually defined without margins, the treatment success critically depends on accurate definition and contouring of the target volume and organs at risk (OARs) which are commonly situated in the proximity of the target making their precise delineation particularly important in order to limit possible normal tissue complications. Subsequent treatment planning is reliant on these volumes, which makes the accurate contouring a requisite to high quality treatments. 

    The purpose of this work was to evaluate the current degree of variability for target and OAR contouring and to establish methods for analysing multi-observer data regarding structure delineation variability. Furthermore, this was set in a broader picture including the importance of contouring studies, the clinical implications of contouring errors and the possible mitigation of the variability in contouring by robust treatment planning.

    A multi-centre target and OAR contouring study was initiated. Four complex and six common cases to be treated with SRS were selected and subsequently distributed to centres around the world performing Gamma Knife® radiosurgery for delineation and treatment planning. The resulting treatment plans and the corresponding delineated structures were collected and analysed.

    Results showed a very high variability in contouring for the four complex radiosurgery targets. Similar results indicating high variability in delineating the common targets and OARs were also reported. This emphasised the need of continuous work towards consistent and standardized SRS treatments. Consequently, the results of the OAR analysis were incorporated in an effort to standardize stereotactic radiosurgery (SRS). Variations in treatment planning were as well analysed for several of the indications included in the initial study on contour delineation and the results showed a high variability in planned doses including several plans presenting large volumes of the brain receiving a higher dose than 12 Gy, indicating an elevated risk of normal tissue complications.

    The results of the contouring work were, as a last step of this thesis, used as input for a robust treatment planning approach considering the variability in target delineation. The very preliminary results indicate the feasibility of the probabilistic approach and the potential of robust treatment planning to account for uncertainties in target extent and location.

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  • 110.
    Sandström, Helena
    Stockholm University, Faculty of Science, Department of Physics.
    Contouring variability in radiosurgery - dosimetric and radiobiological implications2015Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The use of Stereotactic Radiation Therapy (SRT) employing one large fraction of radiation, as in stereotactic radiosurgery (SRS), or few fractions of high doses, has continuously increased due to the technical development and the progress in dose delivery complemented by the positive clinical experience. The success of stereotactic radiation therapy depends on many clinical, dosimetric and radiobiological factors. For SRS in particular, the delivery of a highly conformal dose distribution to the target in one fraction allowing at the same time the sparing of the normal tissue and the critical structures is part of the basic concept of the technique. Provided that the highly accurate radiosurgical equipment available today is used, planning and delivering the prescribed dose distribution is an achievable goal, and therefore the main issue to be solved is the definition of the target. As the target volume in radiosurgery is usually defined without margins, the success of the stereotactic approach critically depends on the accurate delineation of the target which could be identified as a factor of key importance. In addition, the delineation of the Organs At Risk (OAR) is also critical.

    The purpose of this work was to evaluate the current degree of variability for target and OAR contouring and to establish methods for analysing multi-observer data regarding structure delineation variability.

    A multi-center target and OAR delineation study was initiated. Two complex and six common cases to be treated with SRS were selected and subsequently distributed to centers around the world performing Gamma Knife® radiosurgery for delineation and treatment planning. The resulting treatment plans and the corresponding delineated structures were collected and analysed.   

    Results showed a very high variability in contouring for four complex radiosurgery targets. Similar results indicating high variability in delineating the OAR and reporting the doses delivered to them were also reported. For the common radiosurgery targets however, a higher agreement in the delineation was observed, although lower than expected.

    The assessment of the quality of treatment planning for radiosurgery is usually performed with respect to the coverage of the target, the planning specificity, and dose to the sensitive structures and organs close to the target. However, physical dose conformity to the target does not guarantee the success of the treatment. The assessment of the plan quality should also be performed with respect to the clinical outcome expressed as probability of controlling the target that should be irradiated. In this respect, this study also aimed to create the framework for assessing the impact of the inaccuracy in delineating the target on the predicted treatment outcome for radiosurgery targets known for their high potential to invade the neighbouring normal tissue, using radiobiological models. In addition, radiobiological models have also been used to determine the tumour control probability accounting for the oxygenation for stereotactic radiation therapy targets.

    The results suggest that radiobiological modelling has the potential to add to the current knowledge in SRS by theoretically assessing the key factors that might influence the treatment outcome.

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  • 111.
    Sandström, Helena
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Nordström, Håkan
    Chung, Caroline
    Toma-Dasu, Iuliana
    Stockholm University, Faculty of Science, Department of Physics.
    Treatment planning for Gamma Knife radiosurgery – assessment of variability and mitigation through probabilistic robust planningManuscript (preprint) (Other academic)
  • 112.
    Sandström, Helena
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Toma-Dasu, Iuliana
    Stockholm University, Faculty of Science, Department of Physics.
    Chung, Caroline
    Gårding, Jonas
    Jokura, Hidefumi
    Dasu, Alexandru
    Simultaneous truth and performance level estimation method for evaluation of target contouring in radiosurgery – feasibility test and robustness analysis2019In: Physica medica (Testo stampato), ISSN 1120-1797, E-ISSN 1724-191XArticle in journal (Refereed)
  • 113. Schuemann, Jan
    et al.
    Bassler, Niels
    Stockholm University, Faculty of Science, Department of Physics.
    Inaniwa, Taku
    Computational models and tools2018In: Medical physics, ISSN 0094-2405, Vol. 45, no 11, p. e1073-e1085Article in journal (Refereed)
    Abstract [en]

    In this chapter, we describe two different methods, analytical (pencil beam) algorithms and Monte Carlo simulations, used to obtain the intended dose distributions in patients and evaluate their strengths and shortcomings. We discuss the difference between the prescribed physical dose and the biologically effective dose, the relative biological effectiveness (RBE) between ions and photons and the dependence of RBE on the linear energy transfer (LET). Lastly, we show how LET- or RBE-based optimization can be used to improve treatment plans and explore how the availability of multimodality ion beam facilities can be used to design a tumor-specific optimal treatment.

  • 114.
    Scott, Pat
    Stockholm University, Faculty of Science, Department of Physics.
    Searches for Particle Dark Matter: Dark stars, dark galaxies, dark halos and global supersymmetric fits2010Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The identity of dark matter is one of the key outstanding problems in both particle and astrophysics. In this thesis, I describe a number of complementary searches for particle dark matter. I discuss how the impact of dark matter on stars can constrain its interaction with nuclei, focussing on main sequence stars close to the Galactic Centre, and on the first stars as seen through the upcoming James Webb Space Telescope. The mass and annihilation cross-section of dark matter particles can be probed with searches for gamma rays produced in astronomical targets. Dwarf galaxies and ultracompact, primordially-produced dark matter minihalos turn out to be especially promising in this respect. I illustrate how the results of these searches can be combined with constraints from accelerators and cosmology to produce a single global fit to all available data. Global fits in supersymmetry turn out to be quite technically demanding, even with the simplest predictive models and the addition of complementary data from a bevy of astronomical and terrestrial experiments; I show how genetic algorithms can help in overcoming these challenges.

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  • 115. Singers Sørensen, Brita
    et al.
    Bassler, Niels
    Stockholm University, Faculty of Science, Department of Physics.
    Nielsen, Steffen
    Horsman,, Michael R.
    Grzanka, Leszek
    Spejlborg, Harald
    Swakoń, Jan
    Olko, Paweł
    Overgaard, Jens
    Relative biological effectiveness (RBE) and distal edge effects of proton radiation on early damage in vivo2017In: Acta Oncologica, ISSN 0284-186X, E-ISSN 1651-226X, Vol. 56, no 11, p. 1387-1391Article in journal (Refereed)
    Abstract [en]

    Introduction: The aim of the present study was to examine the RBE for early damage in an in vivo mouse model, and the effect of the increased linear energy transfer (LET) towards the distal edge of the spread-out Bragg peak (SOBP).

    Method: The lower part of the right hind limb of CDF1 mice was irradiated with single fractions of either 6 MV photons, 240 kV photons or scanning beam protons and graded doses were applied. For the proton irradiation, the leg was either placed in the middle of a 30-mm SOBP, or to assess the effect in different positions, irradiated in 4 mm intervals from the middle of the SOBP to behind the distal dose fall-off. Irradiations were performed with the same dose plan at all positions, corresponding to a dose of 31.25 Gy in the middle of the SOBP. Endpoint of the study was early skin damage of the foot, assessed by a mouse foot skin scoring system.

    Results: The MDD50 values with 95% confidence intervals were 36.1 (34.2–38.1) Gy for protons in the middle of the SOBP for score 3.5. For 6 MV photons, it was 35.9 (34.5–37.5) Gy and 32.6 (30.7–34.7) Gy for 240 kV photons for score 3.5. The corresponding RBE was 1.00 (0.94–1.05), relative to 6 MV photons and 0.9 (0.85–0.97) relative to 240 kV photons. In the mice group positioned at the SOBP distal dose fall-off, 25% of the mice developed early skin damage compared with 0–8% in other groups. LETd,z = 1 was 8.4 keV/μm at the distal dose fall-off and the physical dose delivered was 7% lower than in the central SOBP position, where LETd,z =1 was 3.3 keV/μm.

    Conclusions: Although there is a need to expand the current study to be able to calculate an exact enhancement ratio, an enhanced biological effect in vivo for early skin damage in the distal edge was demonstrated.

  • 116.
    Skyttner, Sofia
    Stockholm University, Faculty of Science, Department of Physics.
    Assessment of two optimization strategies for pediatric computed tomography examinations: Bismuth shielding & organ-based tube current modulation2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Background: It is well known that pediatric patients are different from adult patients. Not only are children of a smaller physical size, but their anatomy differs as well. They are also more vulnerable to ionizing radiation than adults are, since their larger attributable life-time risk for cancer. This entitles children as extra radiosensitive patients, and special concern should be taken regarding their radiosensitive organs. Computed tomography (CT) examinations inevitably involve exposure of all skin-deep organs although rarely being objects for the diagnostic task. For example, multiple CT head examinations increase the risk of radiation induced cataract in eye lenses. Absorbed dose to these radiosensitive skin-deep organs should therefore be decreased by available optimization strategies in accordance withthe ALARA principle -as low as reasonably achievable- which guides the process of optimization anddose reduction. Two optimization strategies to decrease absorbed dose to skin-deep organs are Bismuth (Bi) shielding and organ-based tube current modulation (organ-based TCM).

    Aim: The aim of this work was to assess two dose optimization strategies for decreasing absorbed dose to skin-deep organs in pediatric CT imaging: Bi shielding and organ-based TCM. The specific patient categories chosen were newborn, one year old and five year old.

    Materials and Methods: Three anthropomorphic phantoms representing newborn, one year old and five year old were scanned with CT protocol parameters selected in accordance with clinical routine for pediatric CT examinations at Karolinska University Hospital in Stockholm. Dose differences from introducing the optimization strategies were obtained by using thermoluminescence dosimeters (TLDs) and metal oxide semiconductor feld effect transistor dosimeters (MOSFETs). Monte Carlo estimated dose values were introduced as a comparison to further establish the validity of the obtained measured values.

    Results: The benefit in decreased radiation dose to anterior skin-deep organs - when applying the optimization strategies - depended on both body region and body size. Bi shielding was more advantageous the smaller and less attenuating the body was. Organ-based TCM was more advantageous, if an increased dose to posterior organs could be accepted. A less attenuating and smaller phantom did not benefit by organ-based TCM due to increased posterior irradiation.

    Conclusions: The general conclusion is that the optimal choice of optimization strategy will depend on both body region being scanned and age. Regarding CT head examinations, pediatric patients of ages between newborn and five year old will benefit most by application of organ-based TCM, if an increased dose to backside head can be justified. Regarding CT thorax examinations, newborn and one year old patients will benefit most by application of Bi shielding, while organ-based TCM is preferable for five year old patients.

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  • 117.
    Smania, Massimiliano
    Stockholm University, Faculty of Science, Department of Physics.
    Bell tests and the no-signalling assumption2018Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Bell's theorem was originally meant for testing fundamental properties of Nature, namely local realism. However, through the years it has become a powerful device for certifying encryption security, randomness, and entanglement among other properties. Especially after the series of loophole-free violation papers at the end of 2015, these applications are becoming more and more relevant. In most of these scenarios, additional assumptions - as fair-sampling - are set forth in order to achieve the required near-optimal violations. However, it turns out that many of the experiments realised so far suffer from apparent signalling. We say “apparent” because we do not believe that the issue comes from actual communication between different measurement stations, but rather, as we show in this work, from systematic issues related to the particular experimental realisation.

    After making a point for the importance of correcting these errors, we identify and address some of the most common sources of signalling in a set of experiments based on single photon polarisation qubits. Finally, we report a reliable CHSH violation which is free from apparent signalling.

    While the core results are contained in the attached Paper I, we first provide the reader with a brief introduction to the concepts involved in this work, in addition to supplementary unpublished experimental work.

  • 118.
    Thomas, Henry
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bassler, Niels
    Stockholm University, Faculty of Science, Department of Physics.
    Ureba, Ana
    Stockholm University, Faculty of Science, Department of Physics.
    Tsubouchi, Toshiro
    Valdman, Alexander
    Siegbahn, Albert
    Stockholm University, Faculty of Science, Department of Physics.
    Development of an interlaced-crossfiring geometry for proton grid therapy2017In: Acta Oncologica, ISSN 0284-186X, E-ISSN 1651-226X, Vol. 56, no 11, p. 1437-1443Article in journal (Refereed)
    Abstract [en]

    Background: Grid therapy has in the past normally been performed with single field photon-beamgrids. In this work, we evaluated a method to deliver grid therapy based on interlacing and crossfiringgrids of mm-wide proton beamlets over a target volume, by Monte Carlo simulations.

    Material and methods: Dose profiles for single mm-wide proton beamlets (1, 2 and 3 mm FWHM) inwater were simulated with the Monte Carlo code TOPAS. Thereafter, grids of proton beamlets weredirected toward a cubic target volume, located at the center of a water tank. The aim was to deliver anearly homogeneous dose to the target, while creating high dose heterogeneity in the normal tissue,i.e., high gradients between valley and peak doses in the grids, down to the close vicinity of thetarget.

    Results: The relative increase of the beam width with depth was largest for the smallest beams(þ6.9mm for 1 mm wide and 150MeV proton beamlets). Satisfying dose coverage of the cubic targetvolume (r< ±5%) was obtained with the interlaced-crossfiring setup, while keeping the grid pattern ofthe dose distribution down to the target (valley-to-peak dose ratio<0.5 less than 1 cm before the tar-get). Center-to-center distances around 7–8 mm between the beams were found to give the best com-promise between target dose homogeneity and low peak doses outside of the target.

    Conclusions: A nearly homogeneous dose distribution can be obtained in a target volume by crossfir-ing grids of mm-wide proton-beamlets, while maintaining the grid pattern of the dose distribution atlarge depths in the normal tissue, close to the target volume. We expect that the use of this methodwill increase the tumor control probability and improve the normal tissue sparing in grid therapy.

  • 119.
    Torsello, Francesco
    Stockholm University, Faculty of Science, Department of Physics.
    Theoretical and numerical bimetric relativity2020Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    General relativity (GR) is the standard physical theory describing gravitational interactions. All astrophysical and cosmological observations are compatible with its predictions, provided that unknown matter and energy components are included. These are called dark matter and dark energy.

    In addition, GR describes the nonlinear self-interaction of a massless spin-2 field. In particle physics, there are both massless and massive fields having spin 0, 1 and 1/2. It is then well-justified to ask whether a mathematically consistent nonlinear theory describing a massive spin-2 field exists.

    The Hassan–Rosen bimetric relativity (BR) is a mathematically consistent theory describing the nonlinear interaction between a massless and a massive spin-2 field. These fields are described by two metrics, out of which only one can be directly coupled to us and determines the geometry we probe.

    Since it includes GR, BR is an extension of it and provides us with new astrophysical and cosmological solutions. These solutions, which may give hints about the nature of dark matter and dark energy, need to be tested against observations in order to support or falsify the theory. This requires predictions for realistic physical systems. One such system is the spherically symmetric gravitational collapse of a dust cloud, and its study is the overarching motivation behind the thesis.

    Studying realistic physical systems in BR requires the solving of the nonlinear equations of motion of the theory. This can be done in two ways: (i) looking for methods that simplify the equations in order to solve them exactly, and (ii) solving the equations numerically.

    The studies reviewed in the thesis provide results for both alternatives. In the first case, the results concern spacetime symmetries (e.g., spherical symmetry) and how they affect particular solutions in BR, especially those describing gravitational collapse. In the second case, inspired by the success of numerical relativity, the results initiate the field of numerical bimetric relativity. The simulations provide us with the first hints about how gravitational collapse works in BR.

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  • 120.
    Torsello, Francesco
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Kocic, Mikica
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Högås, Marcus
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Mörtsell, Edvard
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Covariant BSSN formulation in bimetric relativity2020In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 37, no 2, article id 025013Article in journal (Refereed)
    Abstract [en]

    Numerical integration of the field equations in bimetric relativity is necessary to obtain solutions describing realistic systems. Thus, it is crucial to recast the equations  as a well-posed problem. In general relativity, under certain assumptions, the covariant BSSN formulation is a strongly hyperbolic formulation of the Einstein equations, hence its Cauchy problem is well-posed. In this paper, we establish the covariant BSSN formulation of the bimetric field equations. It shares many features with the corresponding formulation in general relativity, but there are a few fundamental differences between them. Some of these differences depend on the gauge choice and alter the hyperbolic structure of the system of partial differential equations compared to general relativity. Accordingly, the strong hyperbolicity of the system cannot be claimed yet, under the same assumptions as in general relativity. In the paper, we stress the differences compared with general relativity and state the main issues that should be tackled next, to draw a roadmap towards numerical bimetric relativity.

  • 121.
    Volkov, Mikhail
    Stockholm University, Faculty of Science, Department of Physics.
    Solving the quantum scattering problem for systems of two and three charged particles2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    A rigorous formalism for solving the Coulomb scattering problem is presented in this thesis. The approach is based on splitting the interaction potential into a finite-range part and a long-range tail part. In this representation the scattering problem can be reformulated to one which is suitable for applying exterior complex scaling. The scaled problem has zero boundary conditions at infinity and can be implemented numerically for finding scattering amplitudes. The systems under consideration may consist of two or three charged particles.

    The technique presented in this thesis is first developed for the case of a two body single channel Coulomb scattering problem. The method is mathematically validated for the partial wave formulation of the scattering problem. Integral and local representations for the partial wave scattering amplitudes have been derived. The partial wave results are summed up to obtain the scattering amplitude for the three dimensional scattering problem. The approach is generalized to allow the two body multichannel scattering problem to be solved. The theoretical results are illustrated with numerical calculations for a number of models.

    Finally, the potential splitting technique is further developed and validated for the three body Coulomb scattering problem. It is shown that only a part of the total interaction potential should be split to obtain the inhomogeneous equation required such that the method of exterior complex scaling can be applied. The final six-dimensional equation is reduced to a system of three dimensional equations using the full angular momentum representation. Such a system can be numerically implemented using the existing full angular momentum complex exterior scaling code (FAMCES). The code has been updated to solve the three body scattering problem.

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  • 122. Volkwyn, Trevor
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Wikman, Susanne
    Linder, Cedric
    Towards modelling formal learning in terms of the multimodal emergence of transduction2017Conference paper (Refereed)
    Abstract [en]

    Disciplinary learning is a multimodal endeavour that calls for achieving representational competency (Linder et al 2014), which is constituted from the coordination of disciplinary semiotic resources (Airey & Linder, in press). Examples of these semiotic resources for disciplines such as physics and chemistry are mathematics, graphs, gestures, diagrams and language. The effective learning of complex subjects such as these presents many unsolved challenges. In order to begin working towards solving these challenges much still needs to be done to deepen our understanding of how such disciplinary learning takes place. Taking the idea that formal learning is made possible through experiencing specific patterns of variation (Marton 2015), we will use our analysis of student-engagement data to present a case for seeing complex learning in terms of the multimodal emergence (Davis & Sumara, 2006) of transduction (Kress, 2010).  We use these results to propose a model of disciplinary learning that characterizes the multimodal emergence of transduction in terms of the start of a journey towards achieving fluency in a critical constellation of semiotic resources (Airey & Linder 2009; in press) for a given object of learning.

  • 123. Volkwyn, Trevor S.
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Multimodal Transduction in Upper-secondary School Physics2018Conference paper (Other academic)
    Abstract [en]

    In this study we video-filmed upper-secondary physics students working with a laboratory task designed to encourage transduction (Bezemer & Kress 2008) when learning about coordinate systems.

    Students worked in pairs with an electronic measurement device to determine the direction of the Earth’s magnetic field. The device, IOLab, can be held in the hand and moved around. The results of this movement are graphically displayed on a computer screen as changes in the x, y and z components of the Earth’s magnetic field. The students were simply instructed to use the IOLab to find the direction of the Earth’s magnetic field and mark its direction using a red paper arrow.

    A full multimodal transcription of the student interaction was made (Baldry & Thibault 2006). In our analysis of this transcription, three separate transductions of meaning were identified—transduction of meaning potential in the room to the computer screen, transduction of this meaning to the red arrow, and finally transduction into student gestures. We suggest that this final transduction could not have been made without the introduction of the arrow, which functioned as a coordinating hub (Fredlund et al 2012).

    We recommend that teachers should carefully think about the resources in a task that may function as a coordinating hub and should also look for student transductions in their classrooms as confirmation that learning is taking place.

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  • 124. Volkwyn, Trevor S.
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Working with magnetic field to learn about coordinate systems: A social semiotic approach2017Conference paper (Refereed)
    Abstract [en]

    In the teaching and learning of physics, a wide range of semiotic resources are used, such as spoken and written language, graphs, diagrams, mathematics, hands on work with apparatus, etc. (Lemke, 1998). In this respect it has been argued that there is a critical constellation of semiotic resources that is needed for appropriate construction of any given disciplinary concept (Airey & Linder, 2009; Airey, 2009). In this social semiotic tradition, it is the development of “fluency” in the individual semiotic resource systems and the ease of transduction (movement and coordination of meaning) between the various semiotic resource systems that makes disciplinary learning possible. We report here findings from an interpretive study of physics students working with a laboratory task designed to encourage transduction when learning about coordinate systems. A hand-held electronic measurement device (IOLab) was used to display components of the Earth’s magnetic field in real time. Our intention was for students to experience the movability of coordinate systems by open-ended investigation of dynamic, real-time changes in the x, y and z components displayed on the computer screen as they manipulated the device. Building on earlier work of Fredlund et. al. (2012) our analysis identifies three types of transduction, the last of which is transduction of meaning to a new modality (iconic gesture) not previously used by the students. We suggest this final form of transduction is indicative of what students have learned and offers the teacher a chance to confirm/challenge student conceptions. Our data clearly demonstrates how careful, open-ended task design, coupled with timely instructor questions can leverage the pedagogical affordances (Airey, 2015) of a range of semiotic resources to make physics learning possible. We therefore claim that understanding the roles that different semiotic resources play for physics learning is vital and call for further research in this area.

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  • 125. Volkwyn, Trevor S.
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Linder, Cedric
    Coordinating multiple resources to learn physics2017Conference paper (Other academic)
    Abstract [en]

    It has been argued that for any given physics task there is a critical constellation of resources that students need to become proficient in handling in order for physics learning to take place. This is because different resources offer access to different information i.e. they have different pedagogical and disciplinary affordances. A laboratory exercise requiring coordination of multiple resources was designed to help students appreciate the movability of coordinate systems. Initially students were unable to coordinate the manipulation of a hand-held measuring device (IOLab) and observe changes in three readouts on a computer screen, whilst simultaneously drawing conclusions in their discussions with each other and the facilitator. However, the introduction of a paper arrow allowed students to quickly coordinate the resources and begin to experience the movability of coordinate systems. The study confirms earlier work on critical constellations of resources and the functioning of persistent resources as coordinating hubs.

  • 126. Volkwyn, Trevor S.
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Linder, Cedric
    Physics students learning about abstract mathematical tools while engaging with “invisible” phenomena2017Conference paper (Other academic)
    Abstract [en]

    The construction of physics knowledge of necessity entails a range of semiotic resources, (e.g. specialized language, graphs, algebra, diagrams, equipment, gesture, etc.). In this study we documented physics students' use of different resources when working with an "invisible" phenomenon--magnetic field. Using a social semiotic framework, we show how appropriate coordination of resources not only enabled students to learn something about the Earth's magnetic field, but also about the use of an abstract mathematical tool--coordinate systems. Our work leads us to make three suggestions: 

    1. The potential for learning physics can be maximized by designing tasks that encourage students to use a specific set of resources. 

    2. Thought should be put into what this particular set of resources should be and how they may be coordinated.

    3. Close attention to the different resources that students use can allow physics teachers to gauge the learning occurring in their classrooms.

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  • 127. Volkwyn, Trevor S.
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Linder, Cedric
    Teaching the movability of coordinate systems: Discovering disciplinary affordances2017Conference paper (Other academic)
    Abstract [en]

    When students are introduced to coordinate systems in their physics textbooks these are usually oriented in the same manner (x increases to the right). There is a real danger then, that students see coordinate systems as fixed. However, as we know, movability is one of the main disciplinary affordances of coordinate systems. Students worked with an open-ended task to find the direction of Earth’s magnetic field. This was achieved by manipulating a measurement device (IOLab) so as to maximize the signal for one component of the field, whilst at the same time keeping the other two components at zero. In the process of completing this task, students came to experience themselves as holding a movable coordinate system. From this point they spontaneously offer elaborations about the usefulness of purposefully setting up coordinate systems for problem solving. In our terms, they have discovered one of the disciplinary affordances of coordinate systems.

  • 128. Volkwyn, Trevor S.
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Linder, Cedric
    The IOLab and Magnetic Field – Magnetic North Versus Actual Direction2017Conference paper (Other academic)
    Abstract [en]

    Most students will be familiar with the compass as a tool that points north. However, the compass only shows us one component—the terrestrial projection—of the Earth’s magnetic field. In contrast, the IOLab potentially gives students access to the actual direction of the field. We have designed an open-ended task in which pairs of students use the IOLab to determine the actual direction of the Earth’s magnetic field in a laboratory classroom. Without any prior instruction or step-by-step procedure to follow, students simultaneously coordinate a set of resources: speech (in groups; and with facilitator), interpretation of graphical readouts, physical manipulation of the IOLab and proprioception. By coordinating the resources available, the students in our study can be seen to quickly come to a moment of disciplinary insight, where they realize the true direction of the magnetic field.

  • 129. Volkwyn, Trevor S.
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Linder, Cedric J.
    Physics students learning about abstract mathematical tools when engaging with “invisible” phenomena2017In: 2017 Physics Education Research Conference Proceedings / [ed] L. Ding, A. Traxler, Y. Cao, Cincinnati, Ohio: American Association of Physics Teachers , 2017, p. 408-411Conference paper (Refereed)
    Abstract [en]

    The construction of physics knowledge of necessity entails a range of semiotic resources, (e.g. specialized language, graphs, algebra, diagrams, equipment, gesture, etc.). In this study we documented physics students' use of different resources when working with an "invisible" phenomenon--magnetic field. Using a social semiotic framework, we show how appropriate coordination of resources not only enabled students to learn something about the Earth's magnetic field, but also about the use of an abstract mathematical tool--coordinate systems. Our work leads us to make three suggestions: 1. The potential for learning physics can be maximized by designing tasks that encourage students to use a specific set of resources.  2. Thought should be put into what this particular set of resources should be and how they may be coordinated. 3. Close attention to the different resources that students use can allow physics teachers to gauge the learning occurring in their classrooms.

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  • 130. Volkwyn, Trevor Stanton
    et al.
    Airey, John
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education. Uppsala University, Sweden.
    Gregorcic, Bor
    Heijkenskjöld, Filip
    Transduction and Science Learning: Multimodality in the Physics Laboratory2019In: Designs for Learning, ISSN 1654-7608, Vol. 11, no 1, p. 16-29Article in journal (Refereed)
    Abstract [en]

    In this paper we discuss the role of transduction in the teaching and learning of science. We video-filmed pairs of upper-secondary physics students working with a laboratory task designed to encourage transduction (Bezemer & Kress, 2008). The students were simply instructed to use a hand-held electronic measurement device (IOLab) to find the direction of the Earth’s magnetic field and mark its direction using a paper arrow.

    A full multimodal transcription of the student interaction was made. In our analysis of this transcription we identify three separate transductions of meaning. In particular, we observed that student transduction of meaning to the paper arrow allowed it to function as both a persistent placeholder for all the meaning making that had occurred up until that point and as a coordinating hub for further meaning making.

    Our findings lead us to recommend that teachers interrogate the set of resources necessary for appropriate disciplinary knowledge construction in the tasks they present to students. Here, teachers should think carefully about whether the introduction of a persistent placeholder would be useful and in that case what this placeholder could be. We also suggest that teachers should think about what persistent resource may function as a coordinating hub for the students.

    Finally, we suggest that teachers should be on the lookout for student transductions to new semiotic resources in their classrooms as a sign that learning is taking place. We claim that the constraining and complementary nature of transduction offers a good opportunity for teachers to check student understanding, since disciplinary meanings need to be coherent across semiotic systems (modes).

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  • 131.
    Wahlgren, Ulf
    Stockholm University.
    A MO-SCF study of hydroxyl binding and hydroxyl diffusion in pure and fluorine-containing hydroxyapatite1972Doctoral thesis, monograph (Other academic)
  • 132.
    Waltersson, Erik
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Lindroth, Eva
    Stockholm University, Faculty of Science, Department of Physics.
    Pilskog, Ingjald
    Department of Physics and Technology, University of Bergen, N-5020 Bergen, Norway.
    Hansen, Jan Petter
    Department of Physics and Technology, University of Bergen, N-5020 Bergen, Norway.
    Controlled operations in a strongly correlated two-electron quantum ring2009In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 79, no 11, p. 115318-Article in journal (Refereed)
    Abstract [en]

    We have analyzed the electronic spectrum and wave-function characteristics of a strongly correlated two-electron quantum ring with model parameters close to those observed in experiments. The analysis is based on an exact diagonalization of the Hamiltonian in a large B-spline basis. We propose a qubit pair for storing quantum information, where one component is stored in the total electron spin and one multivalued “quMbit” is represented by the total angular momentum. In this scheme the controlled-NOT quantum gate is demonstrated with near 100% fidelity for a realistic far-infrared electromagnetic pulse.

  • 133. Waluyo, Iradwikanari
    et al.
    Nordlund, Dennis
    Bergmann, Uwe
    Pettersson, Lars G.M.
    Stockholm University, Faculty of Science, Department of Physics.
    Nilsson, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Increased Fraction of Weakened Hydrogen Bonds of Water in AOT Reverse Micelles2009In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 131, p. 031103-Article in journal (Refereed)
    Abstract [en]

    Water in aerosol OT reverse micelles has been extensively studied as a model system for nanoconfined water. Results from previous vibrational studies suggest that water confined this way has slower dynamics compared to bulk water; however, the effects on the hydrogen bonding network are unclear. From our study of the structure of water hydrogen bonding using x-ray Raman spectroscopy, we found an increased fraction of weakened hydrogen bonds upon confinement, similar to the effect seen in temperature increase and NaCl solvation, as evidenced by the changes in specific spectral features

  • 134.
    Wesslén, Carl
    Stockholm University, Faculty of Science, Department of Physics.
    Confinement Sensitivity in Quantum Dot Spin Relaxation2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Quantum dots, also known as artificial atoms, are created by tightly confining electrons, and thereby quantizing their energies. They are important components in the emerging fields of nanotechnology where their potential uses vary from dyes to quantum computing qubits. Interesting properties to investigate are e.g. the existence of atom-like shell structures and lifetimes of prepared states.

    Stability and controllability are important properties in finding applications to quantum dots. The ability to prepare a state and change it in a controlled manner without it loosing coherence is very useful, and in some semiconductor quantum dots, lifetimes of up to several milliseconds have been realized. Here we focus on dots in semiconductor materials and investigate how the confined electrons are effected by their experienced potential.

    The shape of the dot will effect its properties, and is important when considering a suitable model. Structures elongated in one dimension, often called nanowires, or shaped as rings have more one-dimensional characteristics than completely round or square dots. The two-dimensional dots investigated here are usually modeled as harmonic oscillators, however we will also consider circular well models.

    The effective potential confining the electrons is investigated both in regard to how elliptical it is, as well as how results differ when using a harmonic oscillator or a circular well potential. By mixing spin states through spin-orbit interaction transitioning between singlet and triplet states becomes possible with spin independent processes such as phonon relaxation. We solve the spin-mixing two-electron problem numerically for some confinement, and calculate the phonon transition rate between the lowest energy singlet and triplet states using Fermi's golden rule.

    The strength of the spin-orbit interaction is varied both by changing the coupling constants, and by applying an external, tilted, magnetic field. The relation between magnetic field parameters and dot parameters are used to maximize state lifetimes, and to model experimental results.

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  • 135.
    Wiklund, Kristin
    Stockholm University, Faculty of Science, Department of Physics.
    Modeling of dose and sensitivity heterogeneities in radiation therapy2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The increased interest in the use of light ion therapy is due to the high dose conformity to the target and the dense energy deposition along the tracks resulting in increased relative biological effectiveness compared to conventional radiation therapy. In spite of the good clinical experience, fundamental research on the characteristics of the ion beams is still needed in order to be able to fully explore their use. Therefore, a Monte Carlo track structure code, KITrack, simulating the transport of electrons in liquid water, has been developed and used for calculation of parameters of interest for beam characterization. The influence of the choice of the cross sections for the physical processes on the electron tracks has also been explored. As an alternative to Monte Carlo calculations a semi-analytical approach to calculate the radial dose distribution from ions, has been derived and validated.

    In advanced radiation therapy, accurate characterization of the beams has to be complemented by comprehensive radiobiological models, which relate the dose deposition into the cells to the outcome of the treatment. The second part of the study has therefore explored the influence of heterogeneity in the dose deposition into the cells as well as the heterogeneity in the cells sensitivity to radiation on the probability of controlling the tumor. Analytical expressions for tumor control probability including heterogeneous dose depositions or variation of radiation sensitivity of cells and tumors have been derived and validated with numerical simulations. The more realistic case of a combination of these effects has also been explored through numerical simulations.

    The MC code KITrack has evolved into an extremely useful tool for beam characterization. The tumor control probability, given by the analytical derived expression, can help improve radiation therapy. A novel anisotropy index has been proposed. It is a measure of the absence of isotropy and provides deeper understanding of the relationship between beam quality and biological effects.

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  • 136. Wiklund, Kristin
    et al.
    Toma-Dasu, Iuliana
    Stockholm University, Faculty of Science, Department of Physics.
    Lind, Bengt K.
    Reply to the comment on ‘The influence of dose heterogeneity on tumour control probability in fractionated radiation therapy’2013In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 58, no 18, p. 6591-6592Article in journal (Other academic)
  • 137.
    With, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Investigations of a beam phase-space modelfor multi-leaf collimated electron fields2010Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
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  • 138. Yakovlev, S. L.
    et al.
    Volkov, Mikhail V.
    Stockholm University, Faculty of Science, Department of Physics.
    Yarevsky, E.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    The impact of sharp screening on the Coulomb scattering problem in three dimensions2010In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 43, no 24, p. 245302-Article in journal (Refereed)
    Abstract [en]

    The scattering problem for two particles interacting via theCoulomb potential isexamined for the case where the potential has a sharp cut-off at some distance.The problem is solved for two complementary situations, firstly, when theinterior part of the Coulomb potential is left in the Hamiltonian and, secondly,when the long-range tail is considered as the potential. The partial wave resultsare summed up to obtain the wavefunction in three dimensions. It is shownthat in the domains where the wavefunction is expected to be proportionalto the known solutions, the proportionality is given by an operator actingon the angular part of the wavefunction. The explicit representation for thisoperator is obtained in the basis of Legendre polynomials. We proposed adriven Schr¨odinger equation including an inhomogeneous term of the finiterange with purely outgoing asymptotics for its solution in the case of thethree-dimensional scattering problem with long-range potentials.

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  • 139.
    Ödén, Jakob
    Stockholm University, Faculty of Science, Department of Physics.
    Proton plan evaluation: a framework accounting for treatment uncertainties and variable relative biological effectiveness2017Licentiate thesis, comprehensive summary (Other academic)
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  • 140.
    Ödén, Jakob
    Stockholm University, Faculty of Science, Department of Physics. RaySearch Laboratories AB, Stockholm, Sweden.
    Relative biological effectiveness in proton therapy: accounting for variability and uncertainties2019Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Radiation therapy is widely used for treatments of malignant diseases. The search for the optimal radiation treatment approach for a specific case is a complex task, ultimately seeking to maximise the tumour control probability (TCP) while minimising the normal tissue complication probability (NTCP). Conventionally, standard curative treatments have been delivered with photons in daily fractions of 2 Gy over a period of approximately three to eight weeks. However, the interest in hypofractionated treatments and proton therapy have rapidly increased during the last decades. Given the same TCP for a photon and a proton plan, the proton plan selection could be made purely based on the reduction in NTCP. Such a plan selection system is clean and elegant but is not flawless. The nominal plans are typically optimised on a single three-dimensional scan of the patient trying to account for the treatment related uncertainties such as particle ranges, patient setup, breathing and organ motion. The comparison also relies on the relative biological effectiveness (RBE), which relates the doses required by photons and protons to achieve the same biological effect. The clinical standard of using a constant proton RBE of 1.1 does not reflect the complex nature of the RBE, which varies with parameters such as linear energy transfer (LET), fractionation dose, tissue type and biological endpoint.

    These aspects of proton therapy planning have been investigated in this thesis through five individual studies. Paper I investigated the impact of including models accounting for the variability of the RBE into the plan comparison between proton and photon prostate plans for various fractionation schedules. In paper II, a method of incorporating RBE uncertainties into the robustness evaluation was proposed. Paper III evaluated the impact of variable RBE models and breathing motion for breast cancer treatments using photons and protons. In Paper IV, a novel optimisation method was proposed, where the number of protons stopping in critical structures is reduced in order to control the enhanced LET and the related RBE. Paper V presented a retrospective analysis with alternative treatment plans for intracranial cases with suspected radiation-induced toxicities.

    The results indicate that the inclusion of variable RBE models and their uncertainties into the proton plan evaluation could lead to differences from the nominal plans made under the assumption of a constant RBE of 1.1 for both target and normal tissue doses. The RBE-weighted dose (DRBE) for high α/β targets (e.g. head and neck (H&N) tumours) was predicted to be slightly lower, whereas the opposite was predicted for low α/β targets (e.g. breast and prostate) in comparison to the nominal DRBE. For most normal tissues, the predicted DRBE were often substantially higher, resulting in higher NTCP estimates for several organs and clinical endpoints. By combining uncertainties in patient setup, range and breathing motion with RBE uncertainties, comprehensive robustness evaluations could be performed. Such evaluations could be included in the plan selection process in order to mitigate potential adverse effects caused by an enhanced RBE. Furthermore, objectives penalising protons stopping in risk organ were proven able to reduce LET, RBE and NTCP for H&N and intracranial tumours. Such approach might be a future optimisation tool in order to further reduce toxicity risks and maximise the benefit of proton therapy.

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  • 141.
    Ödén, Jakob
    et al.
    Stockholm University, Faculty of Science, Department of Physics. RaySearch Laboratories AB, Sweden.
    Toma-Dasu, Iuliana
    Stockholm University, Faculty of Science, Department of Physics. Karolinska Institutet, Sweden.
    Witt Nyström, Petra
    The Skandion Clinic, Sweden.
    Traneus, Erik
    RaySearch Laboratories AB, Sweden.
    Dasu, Alexandru
    The Skandion Clinic, Sweden.
    Spatial correlation of linear energy transfer and relative biological effectiveness with treatment related toxicities following proton therapy for intracranial tumors2020In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 47, no 2, p. 342-351Article in journal (Refereed)
    Abstract [en]

    Purpose: The enhanced relative biological effectiveness (RBE) at the end of the proton range might increase the risk of radiation-induced toxicities. This is of special concern for intracranial treatments where several critical organs at risk (OARs) surround the tumor.  In the light of this, a retrospective analysis of dose-averaged linear energy transfer (LETd) and RBE-weighted dose (DRBE) distributions was conducted for three clinical cases with suspected treatment related toxicities following intracranial proton therapy. Alternative treatment strategies aiming to reduce toxicity risks are also presented.

    Methods: The clinical single-field optimized (SFO) plans were recalculated for 81 error scenarios with a Monte Carlo dose engine. The fractionation DRBE was 1.8 Gy (RBE) in 28 or 30 fractions assuming a constant RBE of 1.1. Two LETd- and α/β-dependent variable RBE models were used for evaluation, including a sensitivity analysis of the α/β parameter. Resulting distributions of DRBE and LETd were analyzed together with normal tissue complication probabilities (NTCPs). Subsequently, four multi-field optimized (MFO) plans, with an additional beam and/or objectives penalizing protons stopping in OARs, were created to investigate the potential reduction of LETd, DRBE and NTCP.

    Results: The two variable RBE models agreed well and predicted average RBE values around 1.3 in the toxicity volumes, resulting in increased near-maximum DRBE of 7-11 Gy (RBE) compared to RBE=1.1 in the nominal scenario. The corresponding NTCP estimates increased from 0.8%, 0.0% and 3.7% (RBE=1.1) to 15.5%, 1.8% and 45.7% (Wedenberg RBE model) for the three patients, respectively. The MFO plans generally allowed for LETd, DRBE and NTCP reductions in OARs, without compromising the target dose. Compared to the clinical SFO plans, the maximum reduction of the near-maximum LETd was 56%, 63% and 72% in the OAR exhibiting the toxicity for the three patients, respectively.

    Conclusions: Although a direct causality between RBE and toxicity cannot be established here, high LETd and DRBE correlated spatially with the observed toxicities, whereas setup and range uncertainties had a minor impact. Individual factors, which might affect the patient-specific radiosensitivity, were however not included in these calculations. The MFO plans using both an additional beam and proton track-end objectives allowed the largest reductions in LETd, DRBE and NTCP, and might be future tools for similar cases.

  • 142.
    Škultéty, Viktor
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Critical behaviour of directed percolation process in the presence of compressible velocity field2017Independent thesis Advanced level (degree of Master (Two Years)), 40 credits / 60 HE creditsStudent thesis
    Abstract [en]

    Renormalization group analysis is a useful tool for studying critical behaviour of stochastic systems. In this thesis, field-theoretic renormalization group will be applied to the scalar model representing directed percolation, known as Gribov model, in presence of the random velocity field. Turbulent mixing will be modelled by the compressible form of stochastic Navier-Stokes equation where the compressibility is described by an additional field related to the density. The task will be to find corresponding scaling properties.

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