| 1. |
- Eriksson, Kjell, et al.
(författare)
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Synthetic photometry for carbon-rich giants : V. Effects of grain-size-dependent dust opacities
- 2023
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 673
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Tidskriftsartikel (refereegranskat)abstract
- Context. The properties and the evolution of asymptotic giant branch (AGB) stars are strongly influenced by their mass loss through a stellar wind. This, in turn, is believed to be caused by radiation pressure due to the absorption and scattering of the stellar radiation by the dust grains formed in the atmosphere. The optical properties of dust are often estimated using the small particle limit (SPL) approximation, and it has been used frequently in modelling AGB stellar winds when performing radiation-hydrodynamics (RHD) simulations.Aims. We aim to investigate the effects of replacing the SPL approximation by detailed Mie calculations of the size-dependent opacities for grains of amorphous carbon forming in C-rich AGB star atmospheres.Methods. We performed RHD simulations for a large grid of carbon star atmosphere+wind models with different effective temperatures, luminosities, stellar masses, carbon excesses, and pulsation properties. Also, a posteriori radiative transfer calculations for many radial structures (snapshots) of these models were done, resulting in spectra and filter magnitudes.Results. We find that, when giving up the SPL approximation, the wind models become more strongly variable and more dominated by gusts, although the average mass-loss rates and outflow speeds do not change significantly; the increased radiative pressure on the dust throughout its formation zone does, however, result in smaller grains and lower condensation fractions (and thus higher gas-to-dust ratios). The photometric K magnitudes are generally brighter, but at V the effects of using size-dependent dust opacities are more complex: brighter for low mass-loss rates and dimmer for massive stellar winds.Conclusions. Given the large effects on spectra and photometric properties, it is necessary to use the detailed dust optical data instead of the simple SPL approximation in stellar atmosphere+wind modelling where dust is formed.
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| 2. |
- Stenström, Christer, et al.
(författare)
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The essential work of fracture in peridynamics
- 2023
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Ingår i: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 242:2, s. 129-152
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Tidskriftsartikel (refereegranskat)abstract
- In this work, the essential work of fracture (EWF) method is introduced for a peridynamic (PD) material model to characterize fracture toughness of ductile materials. First, an analytical derivation for the path-independence of the PD J-integral is provided. Thereafter, the classical J-integral and PD J-integral are computed on a number of analytical crack problems, for subsequent investigation on how it performs under large scale yielding of thin sheets. To represent a highly nonlinear elastic behavior, a new adaptive bond stiffness calibration and a modified bond-damage model with gradual softening are proposed. The model is employed for two different materials: a lower-ductility bainitic-martensitic steel and a higher-ductility bainitic steel. Up to the start of the softening phase, the PD model recovers the experimentally obtained stress-strain response of both materials. Due to the high failure sensitivity on the presence of defects for the lower-ductility material, the PD model could not recover the experimentally obtained EWF values. For the higher-ductility bainitic material, the PD model was able to match very well the experimentally obtained EWF values. Moreover, the J-integral value obtained from the PD model, at the absolute maximum specimen load, matched the corresponding EWF value.
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| 3. |
- Höfner, Susanne, et al.
(författare)
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Dynamic atmospheres and winds of cool luminous giants : II. Gradual Fe enrichment of wind-driving silicate grains
- 2022
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 657
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Tidskriftsartikel (refereegranskat)abstract
- Context. The winds observed around asymptotic giant branch (AGB) stars are generally attributed to radiation pressure on dust formed in the extended dynamical atmospheres of these long-period variables. The composition of wind-driving grains is affected by a feedback between their optical properties and the resulting heating due to stellar radiation.Aims. We explore the gradual Fe enrichment of wind-driving silicate grains in M-type AGB stars to derive typical values for Fe/Mg and to test the effects on wind properties and synthetic spectra.Methods. We present new radiation-hydrodynamical DARWIN models that allow for the growth of silicate grains with a variable Fe/Mg ratio and predict mass-loss rates, wind velocities, and grain properties. Synthetic spectra and other observables are computed a posteriori with the COMA code.Results. The self-regulating feedback between grain composition and radiative heating, in combination with quickly falling densities in the stellar wind, leads to low values of Fe/Mg, typically a few percent. Nevertheless, the new models show distinct silicate features around 10 and 18 microns. Fe enrichment affects visual and near-IR photometry moderately, and the new DARWIN models agree well with observations in (J - K) versus (V - K) and Spitzer color-color diagrams. The enrichment of the silicate dust with Fe is a secondary process, taking place in the stellar wind on the surface of large Fe-free grains that have initiated the outflow. Therefore, the mass-loss rates are basically unaffected, while the wind velocities tend to be slightly higher than in corresponding models with Fe-free silicate dust.Conclusions. The gradual Fe enrichment of silicate grains in the inner wind region should produce signatures observable in mid-IR spectro-interferometrical measurements. Mass-loss rates derived from existing DARWIN models, based on Fe-free silicates, can be applied to stellar evolution models since the mass-loss rates are not significantly affected by the inclusion of Fe in the silicate grains.
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| 4. |
- Stenström, Christer
(författare)
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Modelling of fracture toughness using peridynamics : A Study of J-integral, essential work and homogenisation
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Fracture toughness is one of the most important properties of a material. Being able toaccurately estimate the energy that goes into forming new crack surfaces is essential for the development of new materials, quality assurance, structural monitoring and failure analysis. Fracture toughness parameters are routinely determined by mechanical testing and are often used in numerical tools. Furthermore, fracture toughness is a common property in material specification. Numerical simulation of fracture toughness can reduce the need of mechanical testing and is sometimes the only viable alternative when mechanical testing is not an option, for example in component optimisation and in the assessment of operational structural components. However, complex fracture is a challenge in material modelling, which comes from that a material body is assumed to remain continuous in classical continuum mechanics. Classical continuum mechanics is formulated assuming a continuous body and that spatial derivatives are defined. However, this is not the case at cracks and other dis continuities. Complementing continuum mechanics with supplementary procedures for modelling discontinues can also add further challenges. Besides, the assumption of locality, that each material point only interacts with is immediate neighbouring points, becomes invalid for nanoscale geometries. Thus, fracture cannot easily be modelled. An alternative is therefore of interest. Peridynamics is a nonlocal extension of continuum mechanics with the constitutive model formulated as an integro-differential equation. The advantages of using an integral expression are foremost that long-range forces can be handled and that the theory is valid even in the presence of discontinuities, such as cracks, allowing unguided modelling of fracture. Since damage is introduced to the constitutive model of peridynamics, there is no requirement of supplementary procedures that can add further complications. Due to its nonlocal formulation, the method is also capable of capturing nano-effects. However, the use and reporting of fracture toughness parameters in peridynamics is a routine in its infancy as the method is under development.In this thesis, two fracture toughness methods, the classical J-integral and the essential work of fracture (EWF), are studied with peridynamics. Also, as the nonlocality of peri dynamics give rise to certain boundary effects, e.g. on crack faces, homogenisation is a part of the study. The thesis consists of two parts; an introductory summary with discussion and conclu sions, followed by a series of appended papers. The first paper concerns application of Rice's J-integral on displacement derivatives formulation in peridynamics with comparison to an exact analytical stress-strain-displacement specimen solution. The next two papers concerns homogenisation of a peridynamic bar, to remove the end effects, arisen from the nonlocality of peridynamics, to obtain an elastic behaviour exact to a classical continuum mechanics bar. The fourth paper is an implementation of the J-area integral into peridynamics, with study of various discretisation methods. Thereafter, in the last paper, Rice's J-integral and the nonlocal peridynamic J-integral are compared on various specimens, followed by an extension of the research to study EWF with peridynamics for the first time. The study includes a novel automated calibration at the interparticle bond level to simulate nonlinear elastic behaviour, which subsequently is complemented with softening and used for EWF modelling. As a part of introducing the peridynamic J-integral, the study also includes a proof of path independence.Major findings of the study includes:• The classical J-integral on a displacement derivative formulation gives accurateestimations of fracture toughness in peridynamics.• The peridynamic lD bar can be homogenised to obtain a linear elastic behaviour identical to that of an corresponding continuum mechanics body.• The bond calibration method gives a nonlinear elastic peridynamic model that can accurately recover an experimentally obtained stress-strain response. Up to the start of material softening, the nonlinear elastic model recovered the experimentally obtained stress-strain response of two very different materials; a lower-ductility martensitic-bainitic steel and a higher-ductility bainitic steel.• The nonlinear elastic model were able to match very well the experimentally measured EWF for the higher-ductility bainitic steel.• The J-integral value obtained from the peridynamic model, matched the experimentally obtained EWF value for the higher-ductility bainitic steel.
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| 5. |
- Eriksson, Kjell, et al.
(författare)
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Homogenization of the 1D Peri-static/dynamic Bar with Triangular Micromodulus
- 2021
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Ingår i: Journal of Peridynamics and Nonlocal Modeling. - : Springer. - 2522-896X .- 2522-8978. ; 3:2, s. 85-112
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Tidskriftsartikel (refereegranskat)abstract
- In peridynamics, boundary effects generally appear due to nonlocality of interparticle forces; in particular, end effects are found in 1D bars. In a previous work by Eriksson and Stenström (J Peridyn Nonlocal Model 2(2):205–228, 2020), a simple method to remove end effects in certain types of 1D bars, or to homogenize such bars, was presented for bars with constant micromodulus. In this work, which is a continuation of Eriksson and Stenström (J Peridyn Nonlocal Model 2(2):205–228, 2020), the homogenizing procedure is applied to bars with a linear, or “triangular,” micromodulus. For the examples studied, common in practice, the linear elastic behavior of a homogenized bar, is identical to that of a corresponding classical continuum mechanics bar, independently of the interparticle force range and total number of material points of the bar.
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| 6. |
- Stenström, Christer, et al.
(författare)
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The J-area integral applied in peridynamics
- 2021
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Ingår i: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 228:2, s. 127-142
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Tidskriftsartikel (refereegranskat)abstract
- The J-integral is in its original formulation expressed as a contour integral. The contour formulation was, however, found cumbersome early on to apply in the finite element analysis, for which method the more directly applicable J-area integral formulation was later developed. In a previous study, we expressed the J-contour integral as a function of displacements only, to make the integral directly applicable in peridynamics (Stenström and Eriksson in Int J Fract 216:173–183, 2019). In this article we extend the work to include the J-area integral by deriving it as a function of displacements only, to obtain the alternative method of calculating the J-integral in peridynamics as well. The properties of the area formulation are then compared with those of the contour formulation, using an exact analytical solution for an infinite plate with a central crack in Mode I loading. The results show that the J-area integral is less sensitive to local disturbances compared to the contour counterpart. However, peridynamic implementation is straightforward and of similar scope for both formulations. In addition, discretization, effects of boundaries, both crack surfaces and other boundaries, and integration contour corners in peridynamics are considered.
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| 7. |
- Eriksson, Kjell, et al.
(författare)
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Homogenization of the 1D Peri-static/dynamic Bar with Constant Micromodulus
- 2020
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Ingår i: Journal of Peridynamics and Nonlocal Modeling. - : Springer. - 2522-896X .- 2522-8978. ; 2:2, s. 205-228
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Tidskriftsartikel (refereegranskat)abstract
- Because of the nonlocal interparticle forces inherent in peridynamics, surface, boundary, and end effects appear in 3D, 2D and 1D body problems, respectively. In certain situations, the effect is seen as a disturbance, and various efforts, mostly centering on 2D and 1D problems, have been made to reduce it. A simple method has been derived to remove the end effects in a 1D body by homogenizing the body. When a certain body type, common in practice, is homogenized, its linear elastic behavior, independent of the interparticle force range and with a finite number of material points, in the limit infinite, is identical to that of a corresponding classical continuum mechanics body.
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| 8. |
- Bladh, S., et al.
(författare)
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Carbon star wind models at solar and sub-solar metallicities : a comparative study I. Mass loss and the properties of dust-driven winds
- 2019
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 623
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Tidskriftsartikel (refereegranskat)abstract
- ContextThe heavy mass loss observed in evolved stars on the asymptotic giant branch (AGB) is usually attributed to dust-driven winds, but it is still an open question how much AGB stars contribute to the dust production in the interstellar medium, especially at lower metallicities. In the case of C-type AGB stars, where the wind is thought to be driven by radiation pressure on amorphous carbon grains, there should be significant dust production even in metal-poor environments. Carbon stars can manufacture the building blocks needed to form the wind-driving dust species themselves, irrespective of the chemical composition they have, by dredging up carbon from the stellar interior during thermal pulses.AimsWe investigate how the mass loss in carbon stars is affected by a low-metallicity environment, similar to the Large and Small Magellanic Clouds (LMC and SMC).MethodsThe atmospheres and winds of C-type AGB stars are modeled with the 1D spherically symmetric radiation-hydrodynamical code Dynamic Atmosphere and Radiation-driven Wind models based on Implicit Numerics (DARWIN). The models include a time-dependent description for nucleation, growth, and evaporation of amorphous carbon grains directly out of the gas phase. To explore the metallicity-dependence of mass loss we calculate model grids at three different chemical abundances (solar, LMC, and SMC). Since carbon may be dredged up during the thermal pulses as AGB stars evolve, we keep the carbon abundance as a free parameter. The models in these three different grids all have a current mass of one solar mass; effective temperatures of 2600, 2800, 3000, or 3200 K; and stellar luminosities equal to log L-*/L-circle dot = 3.70, 3.85, or 4.00. ResultsThe DARWIN models show that mass loss in carbon stars is facilitated by high luminosities, low effective temperatures, and a high carbon excess (C-O) at both solar and subsolar metallicities Similar combinations of effective temperature, luminosity, and carbon excess produce outflows at both solar and subsolar metallicities. There are no large systematic differences in the mass-loss rates and wind velocities produced by these wind models with respect to metallicity, nor any systematic difference concerning the distribution of grain sizes or how much carbon is condensed into dust. DARWIN models at subsolar metallicity have approximately 15% lower mass-loss rates compared to DARWIN models at solar metallicity with the same stellar parameters and carbon excess. For both solar and subsolar environments typical grain sizes range between 0.1 and 0.5 mu m, the degree of condensed carbon varies between 5 and 40%, and the gas-to-dust ratios between 500 and 10 000.ConclusionsC-type AGB stars can contribute to the dust production at subsolar metallicities (down to at least [Fe/H] = -1) as long as they dredge up sufficient amounts of carbon from the stellar interior. Furthermore, stellar evolution models can use the mass-loss rates calculated from DARWIN models at solar metallicity when modeling the AGB phase at subsolar metallicities if carbon excess is used as the critical abundance parameter instead of the C/O ratio.
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| 9. |
- Böck, Michelle, et al.
(författare)
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On the interplay between robustness and dynamic planning for adaptive radiation therapy
- 2019
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Ingår i: BIOMEDICAL PHYSICS & ENGINEERING EXPRESS. - : Institute of Physics (IOP). - 2057-1976. ; 5:4
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Tidskriftsartikel (refereegranskat)abstract
- Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during the course of treatment, the authors propose a dynamic framework for robust adaptive radiation therapy in which a variety of robust adaptive treatment strategies are introduced and evaluated. This variety is a result of optimization variables with various degrees of freedom within robust optimization models that vary in their grade of conservativeness. The different degrees of freedom in the optimization variables are expressed through either time-and-uncertainty-scenario-independence, time-dependence or time-and-uncertainty-scenario-dependence, while the robust models are either based on expected value-, worst-case- or conditional value-at-risk-optimization. The goal of this study is to understand which mathematical properties of the proposed robust adaptive strategies are relevant such that the accumulated dose can be steered as close as possible to the prescribed dose as the treatment progresses. We apply a result from convex analysis to show that the robust non-adaptive approach under conditions of convexity and permutation-invariance is at least as good as the time-dependent robust adaptive approach, which implies that the time-dependent problem can be solved by dynamically solving the corresponding time-independent problem. According to the computational study, non-adaptive robust strategies may provide sufficient target coverage comparable to robust adaptive strategies if the occurring uncertainties follow the same distribution as those included in the robust model. Moreover, the results indicate that time-and-uncertainty-scenario-dependent optimization variables are most compatible with worst-case-optimization, while time-and-uncertainty-scenario-independent find their best match with expected value optimization. In conclusion, the authors introduced a novel framework for robust adaptive radiation therapy and identified mathematical requirements to further develop robust adaptive strategies in order to improve treatment outcome in the presence of interfractional uncertainties.
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| 10. |
- Eyer, L., et al.
(författare)
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Gaia Data Release 2 Variable stars in the colour-absolute magnitude diagram
- 2019
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 623
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Tidskriftsartikel (refereegranskat)abstract
- Context. The ESA Gaia mission provides a unique time-domain survey for more than 1.6 billion sources with G less than or similar to 21 mag. Aims. We showcase stellar variability in the Galactic colour-absolute magnitude diagram (CaMD). We focus on pulsating, eruptive, and cataclysmic variables, as well as on stars that exhibit variability that is due to rotation and eclipses. Methods. We describe the locations of variable star classes, variable object fractions, and typical variability amplitudes throughout the CaMD and show how variability-related changes in colour and brightness induce "motions". To do this, we use 22 months of calibrated photometric, spectro-photometric, and astrometric Gaia data of stars with a significant parallax. To ensure that a large variety of variable star classes populate the CaMD, we crossmatched Gaia sources with known variable stars. We also used the statistics and variability detection modules of the Gaia variability pipeline. Corrections for interstellar extinction are not implemented in this article. Results. Gaia enables the first investigation of Galactic variable star populations in the CaMD on a similar, if not larger, scale as was previously done in the Magellanic Clouds. Although the observed colours are not corrected for reddening, distinct regions are visible in which variable stars occur. We determine variable star fractions to within the current detection thresholds of Gaia. Finally, we report the most complete description of variability-induced motion within the CaMD to date. Conclusions. Gaia enables novel insights into variability phenomena for an unprecedented number of stars, which will benefit the understanding of stellar astrophysics. The CaMD of Galactic variable stars provides crucial information on physical origins of variability in a way that has previously only been accessible for Galactic star clusters or external galaxies. Future Gaia data releases will enable significant improvements over this preview by providing longer time series, more accurate astrometry, and additional data types (time series BP and RP spectra, RVS spectra, and radial velocities), all for much larger samples of stars.
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