| 1. |
- Berggren, Martin, et al.
(författare)
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Well-posed variational formulations of Friedrichs-type systems
- 2021
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Ingår i: Journal of Differential Equations. - : Elsevier. - 0022-0396 .- 1090-2732. ; 292, s. 90-131
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Tidskriftsartikel (refereegranskat)abstract
- All finite element methods, as well as much of the Hilbert-space theory for partial differential equations, rely on variational formulations, that is, problems of the type: find u∈V such that a(v,u)=l(v) for each v∈L, where V,L are Sobolev spaces. However, for systems of Friedrichs type, there is a sharp disparity between established well-posedness theories, which are not variational, and the very successful discontinuous Galerkin methods that have been developed for such systems, which are variational. In an attempt to override this dichotomy, we present, through three specific examples of increasing complexity, well-posed variational formulations of boundary and initial–boundary-value problems of Friedrichs type. The variational forms we introduce are generalizations of those used for discontinuous Galerkin methods, in the sense that inhomogeneous boundary and initial conditions are enforced weakly through integrals in the variational forms. In the variational forms we introduce, the solution space is defined as a subspace V of the graph space associated with the differential operator in question, whereas the test function space L is a tuple of L2 spaces that separately enforce the equation, boundary conditions of characteristic type, and initial conditions.
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| 2. |
- Hägg, Linus, et al.
(författare)
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Estimating the neutron yield in a deuterium plasma with the JET neutron camera
- 2023
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Ingår i: Review of Scientific Instruments. - : American Institute of Physics (AIP). - 0034-6748 .- 1089-7623. ; 94:7
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Tidskriftsartikel (refereegranskat)abstract
- The JET neutron camera is a well-established detector system at JET, which has 19 sightlines each equipped with a liquid scintillator. The system measures a 2D profile of the neutron emission from the plasma. A first principle physics method is used to estimate the DD neutron yield that is based on JET neutron camera measurements and is independent of other neutron measurements. This paper details the data reduction techniques, models of the neutron camera, simulations of neutron transport, and detector responses used to this end. The estimate uses a simple parameterized model of the neutron emission profile. The method makes use of the JET neutron camera’s upgraded data acquisition system. It also accounts for neutron scattering near the detectors and transmission through the collimator. These components together contribute to 9% of the detected neutron rate above a 0.5 MeVee energy threshold. Despite the simplicity of the neutron emission profile model, the DD neutron yield estimate falls on average within 10% agreement with a corresponding estimate from the JET fission chambers. The method can be improved by considering more advanced neutron emission profiles. It can also be expanded to estimate the DT neutron yield with the same methodology.
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| 3. |
- Hägg, Linus, et al.
(författare)
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Finita elementberäkningar av KL-skivor i Matlab : Slutrapport
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Den platt- och skivlösare som utvecklats inom projektet Träinnovation i Norr (TiiN) har vidareutvecklats för beräkning av ortotropa skivor och plattor. Den vidareutvecklade lösaren är att betrakta som ett steg på vägen mot det långsiktiga målet att utveckla en enkel men riktig platt- och skivlösare för KL-trä. Plattlösaren har med goda resultat verifierats mot såväl en konstruerad lösning som mot beräkningar i Abaqus. Det har tyvärr inte varit möjligt att inom ramen för projektet verifiera skivlösaren.
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| 4. |
- Hägg, Linus
(författare)
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Matchning av stockar till rätt träd
- 2020
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- I projektet har möjligheten att på individnivå sammankoppla timmersorteringsdata med skördardata undersökts. Syftet med en sådan undersökning är att åstadkomma digitalspårbarhet från skog till såg. En kopplad datamängd har insamlats och använts för att utforma algoritmer för automatisk koppling av timmersorteringsdata och skördardata påindividnivå. Förutsatt att stockar kan sättas samman till stammar med hjälp av timmersorteringsdata gäller att omkring 16% av alla stammar med minst 3 sågstockar medhög säkerhet kan kopplas samman i de två datamängderna. En algoritm för sammansättningav stockar till stammar med hjälp av timmersorteringsdata har också utvecklats men denna bedöms i nuvarande form ej nå tillräcklig prestanda. Potentialen att höja prestandan är dock till stor del ännu outforskad.
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| 5. |
- Hägg, Linus, 1988-, et al.
(författare)
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On the well-posedness of Galbrun's equation
- 2021
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Ingår i: Journal des Mathématiques Pures et Appliquées. - : Elsevier. - 0021-7824 .- 1776-3371. ; 150, s. 112-133
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Tidskriftsartikel (refereegranskat)abstract
- Galbrun's equation, which is a second order partial differential equation describing the evolution of a so-called Lagrangian displacement vector field, can be used to study acoustics in background flows as well as perturbations of astrophysical flows. Our starting point for deriving Galbrun's equation is linearized Euler's equations, which is a first order system of partial differential equations that describe the evolution of the so-called Eulerian flow perturbations. Given a solution to linearized Euler's equations, we introduce the Lagrangian displacement as the solution to a linear first order partial differential equation, where the Eulerian perturbation of the fluid velocity acts as a source term. Our Lagrangian displacement solves Galbrun's equation, provided it is regular enough and that the so-called no-resonance assumption holds. In the case that the background flow is steady and tangential to the domain boundary, we prove existence, uniqueness, and continuous dependence on data of solutions to an initial–boundary-value problem for linearized Euler's equations. For such background flows, we demonstrate that the Lagrangian displacement is well-defined, that the initial datum of the Lagrangian displacement can be chosen in order to fulfill the no-resonance assumption, and derive a classical energy estimate for (sufficiently regular solutions to) Galbrun's equation. Due to the presence of zeroth order terms of indefinite signs in the equations, the energy estimate allows solutions that grow exponentially with time.
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| 6. |
- Hägg, Linus, 1988-
(författare)
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The fW-mean filter framework for topology optimization and analysis of Friedrichs systems
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Part I. Topology optimization is the most general form of design optimization in which the optimal layout of material within a given region of space is to be determined. Filters are essential components of many successful density based topology optimization approaches. The generalized fW-mean filter framework developed in this thesis provides a unified platform for construction, analysis, and implementation of filters. Extending existing algorithms, we demonstrate that under special albeit relevant conditions, the computational complexity of evaluating generalized fW-mean filters and their derivatives is linear in the number of design degrees of freedom. We prove that generalized fW-mean filters guarantee existence of solutions to the penalized minimum compliance problem, the archetypical problem in density based topology optimization. In this problem, the layout of linearly elastic material that minimizes the compliance given static supports and loads is to be determined. We formalize the connection between mathematical morphology and the notion of minimum length scale of a layout of material and thereby provide a theoretical foundation for imposing and assessing minimum length scales in density based topology optimization. Elaborating on the fact that some sequences of generalized fW-mean filters provide differentiable approximations of morphological operators, we devise a method capable of imposing different minimum length scales on the two material phases in minimum compliance problems. Part II. The notion of Friedrichs systems, also known as symmetric positive systems, encompasses many linear models of physical phenomena. The prototype model is Maxwell's equations, which describe the evolution of the electromagnetic field in the presence of electrical charges and currents. In this thesis, we develop well-posed variational formulations of boundary and initial–boundary value problems of Friedrichs systems on bounded domains. In particular, we consider an inhomogeneous initial–boundary value problem that models lossless propagation of acoustic disturbances in a stagnant fluid. Galbrun's equation is a linear second order vector differential equation in the so-called Lagrangian displacement, which was derived to model lossless propagation of acoustic disturbances in the presence of a background flow. Our analysis of Galbrun's equation is centered on the observation that solutions to Galbrun's equation may be formally constructed from solutions to linearized Euler's equations. More precisely, the Lagrangian displacement is constructed as the solution to a transport-type equation driven by the Eulerian velocity perturbation. We present partial results on the well-posedness of Galbrun's equation in the particular case that the background flow is everywhere tangential to the domain boundary by demonstrating mild well-posedness of an initial–boundary value problem for linearized Euler's equations and that our construction of the Lagrangian displacement is well-defined. Moreover, we demonstrate that sufficiently regular solutions to Galbrun's equation satisfy an energy estimate.
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| 7. |
- Marcinkevicius, Benjaminas, et al.
(författare)
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Fuel ion ratio determination using the 14 MeV Tandem neutron spectrometer for JET DTE1 campaign discharges
- 2022
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Ingår i: Fusion engineering and design. - : Elsevier. - 0920-3796 .- 1873-7196. ; 184
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Tidskriftsartikel (refereegranskat)abstract
- This paper investigates the determination of the fuel ion ratio nT/ntot in fusion experiments using two different approaches. The methods are applied to plasma discharges from the deuterium-tritium campaign at the Joint European Torus (JET) in 1997. Multiple discharges have been analysed using data acquired with the Tandem (KM2) neutron spectrometer, using a new neutron spectrometer response function and improved line-of-sight information.The two different approaches were generally similar with the exception of the beam slowing down modelling, handled by two different particle transport codes, namely, TRANSP and PENCIL.The results show that nT/ntot can be determined using Tandem neutron spectrometer data; nT/ntot using both of the approaches are consistent and within the uncertainty for a range of studied discharges.The obtained results support previous studies on nT/ntot determination using neutron spectroscopy. In addition, we have shown that PENCIL can be used instead of TRANSP for a range of discharges which could simplify and speed up the estimation of nT/ntot. The possible limitations of the approach using PENCIL could be investigated using different neutron spectrometer data from the 2021 JET deuterium-tritium campaign.A similar spectrometer like Tandem is planned to be operational at ITER and the results of this paper form the first experimental verification of the capability for nT/ntot measurements with such spectrometers. Further research on this could lead to better understanding of these instruments and their limitations before the start of experiments at ITER.
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| 8. |
- Mousavi, Abbas, et al.
(författare)
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Topology optimization of a waveguide acoustic black hole for enhanced wave focusing
- 2024
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Ingår i: Journal of the Acoustical Society of America. - : Acoustical Society of America (ASA). - 0001-4966 .- 1520-8524. ; 155:1, s. 742-756
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Tidskriftsartikel (refereegranskat)abstract
- The waveguide acoustic black hole (WAB) effect is a promising approach for controlling wave propagation in various applications, especially for attenuating sound waves. While the wave-focusing effect of structural acoustic black holes has found widespread applications, the classical ribbed design of waveguide acoustic black holes (WABs) acts more as a resonance absorber than a true wave-focusing device. In this study, we employ a computational design optimization approach to achieve a conceptual design of a WAB with enhanced wave-focusing properties. We investigate the influence of viscothermal boundary losses on the optimization process by formulating two distinct cases: one neglecting viscothermal losses and the other incorporating these losses using a recently developed material distribution topology optimization technique. We compare the performance of optimized designs in these two cases with that of the classical ribbed design. Simulations using linearized compressible Navier-Stokes equations are conducted to evaluate the wave-focusing performance of these different designs. The results reveal that considering viscothermal losses in the design optimization process leads to superior wave-focusing capabilities, highlighting the significance of incorporating these losses in the design approach. This study contributes to the advancement of WAB design and opens up new possibilities for its applications in various fields.
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| 9. |
- Nocente, M., et al.
(författare)
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Fusion product measurements by nuclear diagnostics in the Joint European Torus deuterium-tritium 2 campaign (invited)
- 2022
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Ingår i: Review of Scientific Instruments. - : American Institute of Physics (AIP). - 0034-6748 .- 1089-7623. ; 93:9
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Tidskriftsartikel (refereegranskat)abstract
- A new deuterium-tritium experimental, DTE2, campaign has been conducted at the Joint European Torus (JET) between August 2021 and late December 2021. Motivated by significant enhancements in the past decade at JET, such as the ITER-like wall and enhanced auxiliary heating power, the campaign achieved a new fusion energy world record and performed a broad range of fundamental experiments to inform ITER physics scenarios and operations. New capabilities in the area of fusion product measurements by nuclear diagnostics were available as a result of a decade long enhancement program. These have been tested for the first time in DTE2 and a concise overview is provided here. Confined alpha particle measurements by gamma-ray spectroscopy were successfully demonstrated, albeit with limitations at neutron rates higher than some 10(17) n/s. High resolution neutron spectroscopy measurements with the magnetic proton recoil instrument were complemented by novel data from a set of synthetic diamond detectors, which enabled studies of the supra-thermal contributions to the neutron emission. In the area of escaping fast ion diagnostics, a lost fast ion detector and a set of Faraday cups made it possible to determine information on the velocity space and poloidal distribution of the lost alpha particles for the first time. This extensive set of data provides unique information for fundamental physics studies and validation of the numerical models, which are key to inform the physics and scenarios of ITER. Published under an exclusive license by AIP Publishing.
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| 10. |
- Olofsson, Dan, et al.
(författare)
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Mera rätt råvara 2.0 : Slutrapport
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- På den japanska limträmarknaden uppskattas den norrländska furan p.g.a. dess utseende såväl som dess höga hållfasthet. Produkten benämns Lamina och har sedan 15 år tillbaka växt från en liten obetydlig andel till att idag stå för ett stort bidrag för många furusågverk i Norrland. Det som skiljer den japanska marknaden mot den europeiska är dess önskemål om speciella längder som vi traditionellt inte tillverkar på sågverken. Ska önskemålen uppfyllas krävs det även att apteringen i skogen följer med. Tyvärr är inte alla stockar tillräckligt bra för att uppfylla de styrkekrav som krävs för den japanska marknaden vilket gör att stockar som inte klarar dessa måste sorteras bort och användas för andra marknader. Resultatet av de bortsorterade stockarna är att dessa då får fel längd för den alternativa marknaden och måste då korrigeras med ett extra avkap. Det är därför det är viktigt att så bra det bara går försöka lokalisera vilka avverkningar som innehåller höga andelar av vissa produkter, i detta fall Lamina, och utifrån den informationen styra aptering mot kundönskemål för att skapa mest möjliga virkesvärde. Inom ramen för projektet Mera Rätt Råvara togs en indikator fram där data från de skogliga systemen, baserat på uppgifter som inhämtats och bedömts i fält i samband med avverkningsplanering, används föra att prediktera hållfastheten. Detta projekt är en förlängning på det arbetet och syftar till att förstå mer om korrelationen mellan trädens egenskaper och sågverksprodukternas egenskaper. Mer specifikt har arbetet handlat om att förfina och utvärdera indikatorn i olika typer av skogar med avseende på framför allt ålder. Projektets resultat visar att indikatorn med god precision klarat av att förutse ifall avverkningen är lämpad för produkter för den japanska marknaden. Av de åtta testavverkningar som gjorts låg sju av dessa med ett utfall på mellan 93 - 99% laminakvalitet i timmersorteringen inom det specifika dimensionsintervallet som produkten tas ut i. Alltså mindre än 7% klarade inte av de japanska kraven. Detta kan jämföras med utfallet under år 2020 utan styrning med hjälp av indikatorn. Där låg utfallet på 74%, vilket innebär att med hjälp av indikatorn kan önskade vedegenskaper anrikas. Vidare visar projektets resultat att gallringsskogar inte alls har de vedegenskaper som krävs för att få ett högt utfall av Lamina. Denna kunskap innebär att gallringar ska apteras på ett annat sätt än slutavverkningar och mot andra typer av slutprodukter. Indikatorn i sig har också förbättrats genom Mera Rätt Råvara 2.0. Ett problem med den befintliga skogliga indikatorn visade sig vara att skogsbeståndens skötselhistorik inte alltid var kända. I den nya indikatorn uteslöts skötselhistoriken som parameter och istället togs fler parametrar som beskriver det faktiska beståndet med i analysen. Den nya indikatorn visade sig också bli något bättre på att prediktera Laminavärdet. Projektet har varit så lyckat att resultaten används idag för att styra apteringen i våra avverkningar så att tillredningen i skogen bättre matchar de kundönskemål som sågverket har att ta hänsyn till.
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