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Micromagnetic tomography (MMT) is an emerging technique in rock and paleomagnetism to determine individual magnetic moments of tomographically defined magnetic source regions within a natural sample by means of surface scans of the magnetic field above the sample. MMT relies on combining large high-resolution data sets from X-ray tomography and magnetic scanning devices, like quantum diamond magnetometers, together with advanced inversion algorithms potentially capable to solve for millions of individual magnetic moment vectors. We here provide an overview of existing algorithms that have been developed to tackle different aspects of MMT-related problems and discuss recent advances and future challenges of MMT.

This study focused on the modeling and simulation of a plasma heat source applied toelectric arc welding. The heat source was modeled in three space dimensions couplingthermal fluid mechanics with electromagnetism. Two approaches were considered forcalculating the magnetic field: i) three-dimensional, and ii) axi-symmetric. The anodeand cathode were treated as boundary conditions. The model was implemented in theopen source CFD software OpenFOAM-1.6.x. The electromagnetic part of the solverwas tested against analytic solution for an infinite electric rod. Perfect agreement wasobtained. The complete solver was tested against experimental measurements for GasTungsten Arc Welding (GTAW) with an axi-symmetric configuration. The shielding gaswas argon with thermodynamic and transport properties covering a temperature rangefrom 200 to 30 000 K. The numerical solutions then depend greatly on the approachused for calculating the magnetic field. The axi-symmetric approach indeed neglectsthe radial current density component, mainly resulting in a poor estimation of the arcvelocity. Various boundary conditions were set on the anode and cathode. Theseconditions, difficult to measure and to estimate a priori, significantly affect the plasmaheat source simulation results. Solution of the temperature and electromagnetic fieldsin the electrodes will thus be included in the forthcoming developments.

This study focused on the modeling and simulation of a plasma heat source applied toelectric arc welding. The heat source was modeled in three space dimensions couplingthermal fluid mechanics with electromagnetism. Two approaches were considered forcalculating the magnetic field: i) three-dimensional, and ii) axi-symmetric. The anodeand cathode were treated as boundary conditions. The model was implemented in theopen source CFD software OpenFOAM-1.6.x. The electromagnetic part of the solverwas tested against analytic solution for an infinite electric rod. Perfect agreement wasobtained. The complete solver was tested against experimental measurements for GasTungsten Arc Welding (GTAW) with an axi-symmetric configuration. The shielding gaswas argon with thermodynamic and transport properties covering a temperature rangefrom 200 to 30 000 K. The numerical solutions then depend greatly on the approachused for calculating the magnetic field. The axi-symmetric approach indeed neglectsthe radial current density component, mainly resulting in a poor estimation of the arcvelocity. Various boundary conditions were set on the anode and cathode. Theseconditions, difficult to measure and to estimate a priori, significantly affect the plasmaheat source simulation results. Solution of the temperature and electromagnetic fieldsin the electrodes will thus be included in the forthcoming developments.

This study focused on the modeling and simulation of a plasma heat source applied toelectric arc welding. The heat source was modeled in three space dimensions couplingthermal fluid mechanics with electromagnetism. Two approaches were considered forcalculating the magnetic field: i) three-dimensional, and ii) axi-symmetric. The anodeand cathode were treated as boundary conditions. The model was implemented in theopen source CFD software OpenFOAM-1.6.x. The electromagnetic part of the solverwas tested against analytic solution for an infinite electric rod. Perfect agreement wasobtained. The complete solver was tested against experimental measurements for GasTungsten Arc Welding (GTAW) with an axi-symmetric configuration. The shielding gaswas argon with thermodynamic and transport properties covering a temperature rangefrom 200 to 30 000 K. The numerical solutions then depend greatly on the approachused for calculating the magnetic field. The axi-symmetric approach indeed neglectsthe radial current density component, mainly resulting in a poor estimation of the arcvelocity. Various boundary conditions were set on the anode and cathode. Theseconditions, difficult to measure and to estimate a priori, significantly affect the plasmaheat source simulation results. Solution of the temperature and electromagnetic fieldsin the electrodes will thus be included in the forthcoming developments.

This study focused on the modeling and simulation of a plasma heat source applied toelectric arc welding. The heat source was modeled in three space dimensions couplingthermal fluid mechanics with electromagnetism. Two approaches were considered forcalculating the magnetic field: i) three-dimensional, and ii) axi-symmetric. The anodeand cathode were treated as boundary conditions. The model was implemented in theopen source CFD software OpenFOAM-1.6.x. The electromagnetic part of the solverwas tested against analytic solution for an infinite electric rod. Perfect agreement wasobtained. The complete solver was tested against experimental measurements for GasTungsten Arc Welding (GTAW) with an axi-symmetric configuration. The shielding gaswas argon with thermodynamic and transport properties covering a temperature rangefrom 200 to 30 000 K. The numerical solutions then depend greatly on the approachused for calculating the magnetic field. The axi-symmetric approach indeed neglectsthe radial current density component, mainly resulting in a poor estimation of the arcvelocity. Various boundary conditions were set on the anode and cathode. Theseconditions, difficult to measure and to estimate a priori, significantly affect the plasmaheat source simulation results. Solution of the temperature and electromagnetic fieldsin the electrodes will thus be included in the forthcoming developments.

This study focuses on the simulation of a plasma arc heat source in the context of electric arc welding. The simulation model was implemented in the open source CFD software OpenFOAM-1.6.x, in three space dimensions, coupling thermal fluid mechanics with electromagnetism. Two approaches were considered for calculating the magnetic field: i) the three-dimensional approach, and ii) the so-called axisymmetric approach. The electromagnetic part of the solver was tested against analytic solution for an infinite electric rod. Perfect agreement was obtained. The complete solver was tested against experimental measurements for Gas Tungsten Arc Welding (GTAW) with an axisymmetric configuration. The shielding gas was argon, and the anode and cathode were treated as boundary conditions. The numerical solutions then depend significantly on the approach used for calculating the magnetic field. The so-called axisymmetric approach indeed neglects the radial current density component, mainly resulting in a poor estimation of the arc velocity. Plasma arc simulations were done for various Ar-x%CO2 shielding gas compositions: pure argon (x=0), pure carbon dioxide (x=100), and mixturesof these two gases with x=1 and 10% in mole. The simulation results clearly show that the presence of carbon dioxide results in thermal arc constriction, and increased maximum arc temperature and velocity. Various boundary conditions were set on the anode and cathode (using argon as shielding gas) to evaluate their influence on the plasma arc. These conditions, difficult to measure and to estimate a priori, significantly affect the heat source simulation results. Solution of the temperature and electromagnetic fields in the anode and cathode will thus be included in the forthcoming developments.

In these lectures we present for the first time a mathematical reconstruction of what might have been Gauss' \textit{own} derivation of the linking number of 1833, and we provide also an alternative, explicit proof of its modern interpretation in terms of degree, signed crossings and intersection number. The reconstruction offered here is entirely based on an accurate study of Gauss' own work on terrestrial magnetism and it is complemented by the independent analysis and discussion made by Maxwell in 1867. Since the linking number interpretations in terms of degree, signed crossings and intersection index play such an important r\^ole in modern mathematical physics, we offer a direct proof of their equivalence, and we provide some examples of linking number computation based on oriented area information. The material presented in these lectures forms an integral part of a paper that will appear in the Journal of Knot Theory and Its Ramifications.

This study focused on the modeling and simulation of a plasma heat source applied toelectric arc welding. The heat source was modeled in three space dimensions couplingthermal fluid mechanics with electromagnetism. Two approaches were considered forcalculating the magnetic field: i) three-dimensional, and ii) axi-symmetric. The anodeand cathode were treated as boundary conditions. The model was implemented in theopen source CFD software OpenFOAM-1.6.x. The electromagnetic part of the solverwas tested against analytic solution for an infinite electric rod. Perfect agreement wasobtained. The complete solver was tested against experimental measurements for GasTungsten Arc Welding (GTAW) with an axi-symmetric configuration. The shielding gaswas argon with thermodynamic and transport properties covering a temperature rangefrom 200 to 30 000 K. The numerical solutions then depend greatly on the approachused for calculating the magnetic field. The axi-symmetric approach indeed neglectsthe radial current density component, mainly resulting in a poor estimation of the arcvelocity. Various boundary conditions were set on the anode and cathode. Theseconditions, difficult to measure and to estimate a priori, significantly affect the plasmaheat source simulation results. Solution of the temperature and electromagnetic fieldsin the electrodes will thus be included in the forthcoming developments.