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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Two-fluid physical modeling of superconducting resonators in the ARTEMIS framework

In this work, we implement a new London equation module for superconductivity in the GPU-enabled ARTEMIS framework, and couple it to a finite-difference time-domain solver for Maxwell's equations. We apply this two-fluid approach to model a superconducting coplanar waveguide (CPW) resonator. We validate our implementation by verifying that the theoretical skin depth and reflection coefficients can be obtained for several superconductive materials, with different London penetration depths, over a range of frequencies. Our convergence studies show that the algorithm is second-order accurate in both space and time, except at superconducting interfaces where the approach is spatially first-order. In our CPW simulations, we leverage the GPU scalability of our code to compare the two-fluid model to more traditional approaches that approximate superconducting behavior and demonstrate that superconducting physics can show comparable performance to the assumption of quasi-infinite conductivity as measured by the Q-factor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas

We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following Du Toit et al. (2018), the scheme transforms mixed-derivative diffusion fluxes (which are responsible for the lack of a discrete maximum principle) into nonlinear advective fluxes, amenable to nonlinear-solver-friendly monotonicity-preserving limiters. The scheme enables accurate multi-dimensional heat transport simulations with up to seven orders of magnitude of heat-transport-coefficient anisotropies with low cross-field numerical error pollution and excellent algorithmic performance, with the number of linear iterations scaling very weakly with grid resolution and grid anisotropy, and scaling with the square-root of the implicit timestep. We propose a multigrid preconditioning strategy based on a lower-order approximation that renders the scheme efficient and scalable under grid refinement. Several numerical tests are presented that display the expected spatial convergence rates and strong algorithmic performance, including fully nonlinear magnetohydrodynamics simulations of kink instabilities in a Bennett pinch in 2D helical geometry and of ITER in 3D toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Gradient-Free Construction of Active Subspaces for Dimension Reduction

Recent developments in the field of reduced order modeling - and in particular, active subspace construction - have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this talk, we discuss a gradient free active subspace algorithm that is feasible for high dimensional parameter spaces where finite-difference techniques are impractical. We illustrate an initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1, for input dimensions up to 7700.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics

Recent developments in the field of reduced-order modeling---and, in particular, active subspace construction---have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high-dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this work, we discuss a gradient-free active subspace algorithm that is feasible for high-dimensional parameter spaces where finite-difference techniques are impractical. This analysis extends the gradient-free algorithm introduced in [A. Lewis, R. Smith, and B. Williams, Comput. Math. Appl., 72 (2016), pp. 1603--1615] in two significant ways: (i) we introduce an initialization algorithm to identify lower-dimensional subspaces of influential directions to seed the gradient-free algorithm for high-dimensional problems, and (ii) we analyze dimension selection criteria to verify the algorithms. Finally, we illustrate the initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1 for input dimensions up to 7700.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simple strategy for the simulation of axially symmetric large-area metasurfaces

Metalenses are composed of nanostructures for focusing light and have been widely explored in many exciting applications. However, their expanding dimensions pose simulation challenges. We propose a method to simulate metalenses in a timely manner using vectorial wave and ray tracing models. We sample the metalens’s radial phase gradient and locally approximate the phase profile by a linear phase response. Each sampling point is modeled as a binary blazed grating, employing the chosen nanostructure, to build a transfer function set. The metalens transmission or reflection is then obtained by applying the corresponding transfer function to the incoming field on the regions surrounding each sampling point. Fourier optics is used to calculate the scattered fields under arbitrary illumination for the vectorial wave method, and a Monte Carlo algorithm is used in the ray tracing formalism. We validated our method against finite-difference time domain simulations at 632 nm, and we were able to simulate metalenses larger than 3000 wavelengths in diameter on a personal computer.

Martins, Augusto (ORCID:0000000295546481)↗
DOE OSTI2017

Multistep inversion workflow for 3D long-offset damped elastic waves in the Fourier domain

We present a new workflow for imaging damped three-dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short-offset and low-frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine-scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite-difference frequency-domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full-waveform inversion workflow is applied to the 3D Marmousi-2 and SEG/EAGE Salt models with long-offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one-third of the maximum offset length at a resolution consistent with the inverted frequencies.

3D full waveform inversion↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Coupled Neutron and Gamma Heating Calculation Based on VARIANT Nodal Transport Method

Accurate determination of temperature distributions in fuel pins and duct walls is essential for fuel-pin performance and assembly bowing analyses. Currently, the multi-assembly, sub-channel analysis code SE2-ANL is used in thermalhydraulic analysis of sodium cooled fast reactors (SFR). SE2- ANL is interfaced with the DIF3D/GAMSOR/DIF3D procedure for coupled neutron and gamma heating calculations, developed at Argonne National Laboratory (ANL). In this procedure, the neutron flux distribution is first calculated using the finite-difference diffusion theory option of the DIF3D code. Using the neutron flux solution, the GAMSOR code computes the gamma source distribution for the subsequent gamma flux calculation with DIF3D. However, in the current heating calculation scheme, the neutron and gamma flux calculations are limited to six triangular meshes per hexagonal assembly. In addition, the pin power distributions are estimated by assuming that the power distribution within an assembly is separable in the radial and axial directions. In each assembly, the axial power profile is obtained by averaging the power densities of six triangular meshes at each axial mesh interval. The radial power profile is evaluated at a single axial mesh (e.g., at the core mid-plane) by approximating the neutron and gamma flux distributions by a linear or quadratic polynomial of two variables x and y, depending on the polynomial order specified by the user. The coefficients of the linear and quadratic polynomials are determined by the least squares fit of six and 24 triangular mesh fluxes, respectively. Furthermore, the total heat generation rate in an assembly duct wall is simply determined by a user-specified fraction of the total gamma heating within that assembly. With the advancement of computer technology, the nodal transport theory code VARIANT is routinely used in core design analyses of SFR instead of DIF3D. It is therefore necessary to develop a new heating calculation procedure based on VARIANT neutron and gamma transport calculations. In this study, a new, coupled neutron and gamma heating calculation scheme has been developed to determine the pin power distributions more accurately by eliminating the aforementioned limitations of the current procedure. For this, the GAMSOR code has been extended to generate the intra-nodal gamma source distribution to be consistent with the trial functions of VARIANT. In the new heating calculation procedure, the neutron flux distribution is determined first by solving an eigenvalue transport problem using VARIANT. The obtained neutron flux is then used in GAMSOR to calculate the gamma source distribution. Using this gamma source distribution, the gamma flux distribution is determined by solving a fixed-source transport problem using VARIANT again. Using the computed neutron and gamma flux distributions, the power distribution in each fuel pin and duct wall is determined using a new utility code CURVE, which has been developed to evaluate the VARIANT flux solution at each fuel pin position and along the duct mid-wall. For each pin segment contained in a VARIANT node, the axial power shape is represented as a quadratic profile. The performance of the new heating calculation scheme based on VARIANT transport solutions has been tested against the existing method of SE2-ANL, using the ABR-1000 metal core design. The gamma source distribution and the assembly, fuel pin and duct wall power distributions were calculated and compared. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗
DOE OSTI2017

The effects of nearby fractures on hydraulically induced fracture propagation and permeability changes

Fracture propagation caused by hydraulic fracturing operations can be significantly influenced by adjacent fractures. In this paper, we present a detailed coupled hydro-mechanical analysis to study the effects of nearby natural fractures on hydraulically induced fracture propagation and changes in fracture permeability. Two rock domains were considered in comparison: FD1, with one fracture, and FD2, with two adjacent parallel or non-parallel fractures. It was assumed that water injection occurred in a borehole that intersected the single fracture in FD1 and one of the two fractures in FD2. Simulations were made for a time period of 3 h with an injection period of 2 h followed by 1 h of shut-in. An elastic-brittle model based on the degradation of material properties was implemented in a 2D finite-difference scheme and used for elements of the intact rock subjected to tension and shear failure. The intact rock was considered to have a low but non-negligible permeability. A verification study against analytical solutions showed that the fracture propagation and stress concentrations due to differential boundary stresses could be accurately represented by our model. Next, a base case was considered, in which the stress ratio (SR) between the magnitudes of the maximum and minimum boundary stresses, the permeability k R of the intact rock and the initial permeability k TF of the tension failure regions were fixed. In FD2, the distance d F between the two natural fractures defined by the closest distance was also fixed. The results showed that in both rock domains, the fracture started to propagate when the pore pressure was approximately 85% of the magnitude of the minimum boundary stress. The propagation of a single fracture was significantly greater than the propagation of a double fracture system because, in the latter case, the pore pressure decreased when the two fractures connected. As a result, changes in permeability in FD2 were smaller than in FD1. At the end of injection, the maximum ratios between the final and initial permeability of the natural fractures were found to be approximately 3 and 2 for rock domains FD1 and FD2, respectively. For non-parallel fractures, the controlling factor for fracture propagation was the separation between the tips of the pressurised fracture and the neighbouring non-pressurised fracture. A sensitivity study was conducted to study the influence of the key parameters d F , SR, k R and k TF on the simulation results. Lastly, fracture propagation showed more sensitivity to dF and SR than to the other parameters.

58 GEOSCIENCES↗
DOE OSTI2016

A fast marching algorithm for the factored eikonal equation

The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. This inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modeling and inversion by Gauss–Newton.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Implications for jet noise reduction and turbulence control in general are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

FDTD modeling of induced polarization phenomena in transient electromagnetics

The finite-difference time-domain scheme is augmented in order to treat the modelling of transient electromagnetic signals containing induced polarization effects from 3-D distributions of polarizable media. Compared to the non-dispersive problem, the discrete dispersive Maxwell system contains costly convolution operators. Key components to our solution for highly digitized model meshes are Debye decomposition and composite memory variables. We revert to the popular Cole-Cole model of dispersion to describe the frequency-dependent behaviour of electrical conductivity. Its inversely Laplace-transformed Debye decomposition results in a series of time convolutions between electric field and exponential decay functions, with the latter reflecting each Debye constituents' individual relaxation time. Finally, these function types in the discrete-time convolution allow for their substitution by memory variables, annihilating the otherwise prohibitive computing demands. Numerical examples demonstrate the efficiency and practicality of our algorithm.

58 GEOSCIENCES↗
DOE OSTI2021

Seismic waves in medium with poroelastic/elastic interfaces: a two-dimensional P-SV finite-difference modelling

SUMMARY We present a new methodology of the finite-difference (FD) modelling of seismic wave propagation in a strongly heterogeneous medium composed of poroelastic (P) and (strictly) elastic (E) parts. The medium can include P/P, P/E and E/E material interfaces of arbitrary shapes. The poroelastic part can be with (i) zero resistive friction, (ii) non-zero constant resistive friction or (iii) JKD model of the frequency-dependent permeability and resistive friction. Our FD scheme is capable of subcell resolution: a material interface can have an arbitrary position in the spatial grid. The scheme keeps computational efficiency of the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces). Numerical tests against independent analytical, semi-analytical and spectral-element methods prove the efficiency and accuracy of our FD modelling. In numerical examples, we indicate effect of the P/E interfaces for the poroelastic medium with a constant resistive friction and medium with the JKD model of the frequency-dependent permeability and resistive friction. We address the 2-D P-SV problem. The approach can be readily extended to the 3-D problem.

58 GEOSCIENCES↗
DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Double absorbing boundaries for finite-difference time-domain electromagnetics

We describe the implementation of optimal local radiation boundary condition sequences for second order finite difference approximations to Maxwell's equations and the scalar wave equation using the double absorbing boundary formulation. Numerical experiments are presented which demonstrate that the design accuracy of the boundary conditions is achieved and, for comparable effort, exceeds that of a convolution perfectly matched layer with reasonably chosen parameters. An advantage of the proposed approach is that parameters can be chosen using an accurate a priori error bound.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Finite-frequency modeling of regional tropospheric infrasound using realistic atmospheres and terrain

Infrasonic waves have been observed to propagate to regional (greater than 15 km) distances through the troposphere. Infrasound propagation in the geometric acoustics approximation has shown that realistic terrain can scatter acoustic energy from tropospheric ducts; however, ray methods cannot intrinsically capture finite-frequency behavior such as diffraction. A two-dimensional finite-difference time-domain (FDTD) method has been developed to solve linearized equations for infrasound propagation with realistic terrain. Acoustic wave propagation over 100 km with both flat terrain and a Gaussian hill was first simulated in order to compare finite-frequency propagation with ray predictions. The effects of realistic terrain and atmospheres on infrasound signals from a 2012 surface explosion at the Utah Testing and Training Range are then investigated. Propagation through the troposphere is suggested by array processing results, but eigenrays are not predicted due to weak to nonexistent ducting conditions. FDTD modeling suggests that the inclusion of terrain and finite frequency effects helps explain much of the observed signal in a realistic scenario. Furthermore, these results suggest that geometric acoustics may underestimate propagation through the troposphere, and that recorded waveforms at regional distances may be noticeably affected by terrain.

58 GEOSCIENCES↗
DOE OSTI2023

Acoustic Codes in 2D Spherical Coordinate

Finite-difference methods are widely used to simulate infrasound propagation in the atmosphere. Flexibility of finite-difference scheme allows implementation of highly heterogeneous media for sound propagation as well as complex source models for sound generation. While full 3-D finite-difference methods have been utilized for local infrasound propagation with pronounced topography, 2-D modeling approach has been preferred for regional and global propagation as full 3-D methods generally require enormous computational resources. Infrasound propagation is often simulated with a second-order finite difference scheme. This lowest-order finite-difference scheme is robust and straightforward to implement complex boundary conditions, but the solution includes large error with numerical dispersion and dissipation. This large numerical error may make the second-order finite-difference not optimal for long range infrasound propagation modeling as the numerical dispersion degrades the accuracy of the solution unacceptably. Here, we developed a high-order finite-difference solver for long-range infrasound simulation. The high-order scheme is particularly popular for linear wave modeling in aeroacoustics owing to its low-dispersive and low-dissipative behavior. We develop and evaluate a high-order finite difference scheme in 2-D axisymmetric coordinates. The axisymmetry allows to approximate 3-D spherical sound propagation and amplitude attenuation by a 2-D method. AC2Dr is developed to simulate infrasound propagation in realistic atmosphere, but can be used for linear acoustic waves in general materials with background flow. AC2Dr in an axisymmetric coordinates allows for spherical radiation of acoustic waves from compact sources.

Sjogreen, Bjorn↗